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index.html
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<!DOCTYPE html>
<!-- Created by pdf2htmlEX (https://github.com/pdf2htmlEX/pdf2htmlEX) -->
<html xmlns="https://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8"/>
<meta name="generator" content="pdf2htmlEX"/>
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"/>
<link rel="stylesheet" href="base.min.css"/>
<link rel="stylesheet" href="fancy.min.css"/>
<link rel="stylesheet" href="index.css"/>
<link rel="icon" type="image/png" href="./favicon.png">
<script>
/*
Copyright 2012 Mozilla Foundation
Copyright 2013 Lu Wang <[email protected]>
Apachine License Version 2.0
*/
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(function(){/*
pdf2htmlEX.js: Core UI functions for pdf2htmlEX
Copyright 2012,2013 Lu Wang <[email protected]> and other contributors
https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
*/
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<script>
try{
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}catch(e){}
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<title>50 Lecciones de Matemática - Prof. Evidio Quintana Fernández</title>
</head>
<body>
<div id="sidebar">
<div id="outline">
<ul><li><a class="l" href="#pf4" data-dest-detail='[4,"XYZ",101.905,690.795,null]'>50 Lecciones de Matemática</a><ul><li><a class="l" href="#pf4" data-dest-detail='[4,"XYZ",101.905,551.318,null]'>Lección #1 - Conozcamos al triángulo rectángulo</a></li><li><a class="l" href="#pf7" data-dest-detail='[7,"XYZ",101.905,690.795,null]'>Lección #2 - Rectas y Puntos Notables</a></li><li><a class="l" href="#pfa" data-dest-detail='[10,"XYZ",101.905,690.795,null]'>Lección #3 - Circunferencia y Cuadrilátero</a></li><li><a class="l" href="#pfd" data-dest-detail='[13,"XYZ",101.905,690.795,null]'>Lección #4 - Otros Teoremas</a></li><li><a class="l" href="#pf11" data-dest-detail='[17,"XYZ",101.905,690.795,null]'>Lección #5</a></li><li><a class="l" href="#pf15" data-dest-detail='[21,"XYZ",101.905,690.795,null]'>Lección #6</a></li></ul></li></ul></div>
</div>
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class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">50<span class="_ _0"> </span>Lecciones<span class="_ _0"> </span>de<span class="_ _0"> </span>Matem´<span class="_ _1"></span>atica</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">Prof.<span class="_ _2"> </span>Evidio<span class="_ _2"> </span>Quin<span class="_ _3"></span>tana<span class="_ _2"> </span>F<span class="_ _4"></span>ern´<span class="_ _5"></span>andez</div><div class="t m0 x3 h4 y3 ff2 fs1 fc0 sc0 ls0 ws0">Lecciones<span class="_ _6"> </span>para<span class="_ _6"> </span>la<span class="_ _6"> </span>preparaci´<span class="_ _7"></span>on</div><div class="t m0 x4 h4 y4 ff2 fs1 fc0 sc0 ls0 ws0">en<span class="_ _6"> </span>concursos<span class="_ _6"> </span>de<span class="_ _6"> </span>matem´<span class="_ _7"></span>atica</div><div class="t m0 x5 h4 y5 ff2 fs1 fc0 sc0 ls0 ws0">y<span class="_ _6"> </span>similares</div><div class="t m0 x6 h5 y6 ff3 fs2 fc0 sc0 ls0 ws0">La<span class="_ _8"> </span>Habana</div><div class="t m0 x7 h5 y7 ff3 fs2 fc0 sc0 ls0 ws0">Cuba</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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class="t m0 x8 h6 y8 ff4 fs3 fc0 sc0 ls0 ws0">i</div><div class="t m0 x9 h7 y9 ff5 fs3 fc0 sc0 ls0 ws0">Resumen</div><div class="t m0 xa h7 ya ff6 fs3 fc0 sc0 ls0 ws0">Este<span class="_ _8"> </span>do<span class="_ _9"></span>cumen<span class="_ _3"></span>to<span class="_ _6"> </span>es<span class="_ _8"> </span>una<span class="_ _6"> </span>transcripci´<span class="_ _a"></span>on<span class="_ _8"> </span>de<span class="_ _6"> </span>las<span class="_ _8"> </span>lecciones<span class="_ _6"> </span>del<span class="_ _8"> </span>profesor<span class="_ _6"> </span>Evidio<span class="_ _8"> </span>Quintana</div><div class="t m0 xb h7 yb ff6 fs3 fc0 sc0 ls0 ws0">F<span class="_ _b"></span>ern´<span class="_ _a"></span>andez<span class="_"> </span>para<span class="_ _c"> </span>la<span class="_ _c"> </span>preparaci´<span class="_ _d"></span>on<span class="_ _c"> </span>de<span class="_"> </span>estudiantes<span class="_ _e"> </span>de<span class="_ _e"> </span>preuniversitario<span class="_"> </span>en<span class="_ _c"> </span>concursos<span class="_ _e"> </span>y<span class="_ _e"> </span>similares</div><div class="t m0 xb h7 yc ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>matem´<span class="_ _d"></span>atica.</div><div class="t m0 xa h7 yd ff6 fs3 fc0 sc0 ls0 ws0">Esto<span class="_ _f"> </span>es<span class="_ _f"> </span>un<span class="_ _f"> </span>traba<span class="_ _9"></span>jo<span class="_ _f"> </span>en<span class="_ _f"> </span>progreso,<span class="_ _f"> </span>puede<span class="_ _f"> </span>cambiar<span class="_ _c"> </span>y<span class="_ _f"> </span>tener<span class="_ _f"> </span>errores.<span class="_ _f"> </span>T<span class="_ _b"></span>o<span class="_ _9"></span>do<span class="_ _f"> </span>el<span class="_ _f"> </span>traba<span class="_ _9"></span>jo<span class="_ _f"> </span>y<span class="_ _f"> </span>las</div><div class="t m0 xb h7 ye ff6 fs3 fc0 sc0 ls0 ws0">colecciones<span class="_ _c"> </span>aqu<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>presen<span class="_ _12"></span>tes<span class="_ _c"> </span>son<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>autor<span class="_ _10"></span>´<span class="_ _11"></span>ıa<span class="_ _c"> </span>del<span class="_ _c"> </span>profesor<span class="_ _c"> </span>Evidio.</div><div class="t m0 xa h7 yf ff6 fs3 fc0 sc0 ls0 ws0">Mas<span class="_"> </span>informaci´<span class="_ _a"></span>on<span class="_"> </span>en<span class="_"> </span><span class="fc1">https://gith<span class="_ _3"></span>ub.com/jjavierdguezas/evidio-problemas-matematica<span class="fc0">.</span></span></div><div class="t m0 xb h7 y10 ff6 fs3 fc0 sc0 ls0 ws0">¡Las<span class="_ _c"> </span>con<span class="_ _12"></span>tribuciones<span class="_ _c"> </span>son<span class="_ _c"> </span>bienv<span class="_ _3"></span>enidas!</div><a class="l" href="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/jjavierdguezas/evidio-problemas-matematica"><div class="d m1" style="border-style:none;position:absolute;left:358.140654px;bottom:975.246222px;width:311.023000px;height:12.902000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xc h6 y8 ff4 fs3 fc0 sc0 ls0 ws0">ii</div><div class="t m0 xd h2 y11 ff1 fs0 fc0 sc0 ls0 ws0">´</div><div class="t m0 xb h2 ye ff1 fs0 fc0 sc0 ls0 ws0">Indice</div><div class="t m0 xb h7 y12 ff5 fs3 fc1 sc0 ls0 ws0">50<span class="_ _f"> </span>Lecciones<span class="_ _13"> </span>de<span class="_ _f"> </span>Matem´<span class="_ _14"></span>atica<span class="_ _15"> </span><span class="fc0">1</span></div><div class="t m0 xa h7 y13 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#1<span class="_ _c"> </span>-<span class="_ _f"> </span>Conozcamos<span class="_ _e"> </span>al<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _c"> </span>rect´<span class="_ _d"></span>angulo<span class="_ _6"> </span><span class="fc0">.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _17"> </span>1</span></div><div class="t m0 xa h7 y14 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#2<span class="_ _c"> </span>-<span class="_ _f"> </span>Rectas<span class="_ _e"> </span>y<span class="_ _c"> </span>Puntos<span class="_ _e"> </span>Notables<span class="_ _18"> </span><span class="fc0">.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _17"> </span>4</span></div><div class="t m0 xa h7 y15 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#3<span class="_ _c"> </span>-<span class="_ _f"> </span>Circunferencia<span class="_ _e"> </span>y<span class="_ _c"> </span>Cuadril´<span class="_ _a"></span>atero<span class="_ _19"> </span><span class="fc0">.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _1a"> </span>7</span></div><div class="t m0 xa h7 y16 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#4<span class="_ _c"> </span>-<span class="_ _f"> </span>Otros<span class="_ _e"> </span>T<span class="_ _b"></span>eoremas<span class="_ _1b"> </span><span class="fc0">.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _1c"> </span>10</span></div><div class="t m0 xa h7 y17 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#5<span class="_ _1d"> </span><span class="fc0">.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _1c"> </span>14</span></div><div class="t m0 xa h7 y18 ff6 fs3 fc1 sc0 ls0 ws0">Lecci´<span class="_ _d"></span>on<span class="_ _c"> </span>#6<span class="_ _1d"> </span><span class="fc0">.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _16"> </span>.<span class="_ _6"> </span>.<span class="_ _16"> </span>.<span class="_ _1c"> </span>18</span></div><a class="l" href="#pf4" data-dest-detail='[4,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:168.841203px;bottom:888.202876px;width:156.902000px;height:9.569000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pf4" data-dest-detail='[4,"XYZ",101.905,551.318,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:861.983791px;width:238.023000px;height:11.689000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pf7" data-dest-detail='[7,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:839.313569px;width:190.205000px;height:11.689000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pfa" data-dest-detail='[10,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:816.643346px;width:208.932000px;height:11.689000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pfd" data-dest-detail='[13,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:793.971451px;width:142.629000px;height:11.690000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pf11" data-dest-detail='[17,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:771.301229px;width:56.083000px;height:11.690000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" href="#pf15" data-dest-detail='[21,"XYZ",101.905,690.795,null]'><div class="d m1" style="border-style:none;position:absolute;left:196.221490px;bottom:748.631007px;width:56.083000px;height:11.690000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 xb h2 ye ff1 fs0 fc0 sc0 ls0 ws0">50<span class="_ _0"> </span>Lecciones<span class="_ _0"> </span>de<span class="_ _0"> </span>Matem´<span class="_ _1"></span>atica</div><div class="t m0 xb h5 y19 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#1<span class="_ _6"> </span>-<span class="_ _16"> </span>Conozcamos<span class="_ _6"> </span>al<span class="_ _16"> </span>tri´<span class="_ _7"></span>angulo<span class="_ _6"> </span>rect´<span class="_ _7"></span>angulo</div><div class="t m0 xa h7 y1a ff6 fs3 fc0 sc0 ls0 ws0">Cualquier<span class="_ _c"> </span>estudiante<span class="_ _c"> </span>de<span class="_ _f"> </span>ense˜<span class="_ _d"></span>nanza<span class="_ _f"> </span>media<span class="_ _c"> </span>sab<span class="_ _9"></span>e<span class="_ _c"> </span>que<span class="_ _f"> </span>se<span class="_ _c"> </span>trata<span class="_ _f"> </span>de<span class="_ _c"> </span>un<span class="_ _f"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _f"> </span>que<span class="_ _c"> </span>tiene</div><div class="t m0 xb h7 y1b ff6 fs3 fc0 sc0 ls0 ws0">un<span class="_ _c"> </span>´<span class="_ _d"></span>angulo<span class="_ _f"> </span>con<span class="_ _e"> </span>amplitud<span class="_ _c"> </span>90</div><div class="t m0 xf h8 y1c ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x10 h7 y1b ff6 fs3 fc0 sc0 ls0 ws0">.<span class="_ _c"> </span>Sin<span class="_ _c"> </span>embargo<span class="_ _e"> </span>no<span class="_ _c"> </span>muc<span class="_ _3"></span>hos<span class="_ _c"> </span>sab<span class="_ _9"></span>en<span class="_ _e"> </span>la<span class="_ _f"> </span>can<span class="_ _3"></span>tidad<span class="_ _c"> </span>de<span class="_ _c"> </span>relaciones<span class="_ _c"> </span>que</div><div class="t m0 xb h7 y1d ff6 fs3 fc0 sc0 ls0 ws0">se<span class="_ _f"> </span>generan<span class="_ _f"> </span>en<span class="_ _f"> </span>ese<span class="_ _13"> </span>pol<span class="_ _10"></span>´<span class="_ _11"></span>ıgono.<span class="_ _f"> </span>Dediquemos<span class="_ _13"> </span>en<span class="_ _3"></span>tonces<span class="_ _f"> </span>un<span class="_ _13"> </span>tiempo<span class="_ _13"> </span>al<span class="_ _f"> </span>estudio<span class="_ _f"> </span>de<span class="_ _f"> </span>este<span class="_ _f"> </span>tri´<span class="_ _a"></span>angulo</div><div class="t m0 xb h7 y1e ff6 fs3 fc0 sc0 ls0 ws0">tan<span class="_ _c"> </span>“generoso”.</div><div class="t m0 x11 h9 y1f ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x12 h9 y20 ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x12 h9 y21 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x13 h9 y22 ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">α</span></div><div class="t m0 x14 h9 y23 ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">β</span></div><div class="t m0 x15 h7 y24 ff6 fs3 fc0 sc0 ls0 ws0">1)<span class="_ _c"> </span><span class="ff5">T<span class="_ _10"></span>eorema<span class="_ _13"> </span>de<span class="_ _f"> </span>Pit´<span class="_ _14"></span>agoras</span></div><div class="t m0 x16 h9 y25 ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x17 ha y26 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x18 h7 y25 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x19 ha y26 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h7 y25 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x1b ha y26 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x15 h7 y27 ff6 fs3 fc0 sc0 ls0 ws0">2)<span class="_ _c"> </span><span class="ff5">Razones<span class="_ _f"> </span>T<span class="_ _b"></span>rigonom´<span class="_ _14"></span>etricas</span></div><div class="t m0 x1c h7 y28 ff6 fs3 fc0 sc0 ls0 ws0">sen<span class="_ _1f"> </span><span class="ff8">α<span class="_ _20"> </span></span>=</div><div class="t m0 x1d h9 y29 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x1d h9 y2a ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x1e h7 y2b ff6 fs3 fc0 sc0 ls0 ws0">cos<span class="_ _1f"> </span><span class="ff8">α<span class="_ _20"> </span></span>=</div><div class="t m0 x1d h9 y2c ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1d h9 y2d ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x1c h7 y2e ff6 fs3 fc0 sc0 ls0 ws0">tan<span class="_ _1f"> </span><span class="ff8">α<span class="_ _20"> </span></span>=</div><div class="t m0 x1d h9 y2f ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x1d h9 y30 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1c h7 y31 ff6 fs3 fc0 sc0 ls0 ws0">sen<span class="_ _1f"> </span><span class="ff8">α<span class="_ _20"> </span></span>=<span class="_"> </span>cos<span class="_ _1f"> </span><span class="ff8">β</span></div><div class="t m0 xa h7 y32 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _c"> </span>V<span class="_ _b"></span>ea<span class="_ _f"> </span>que<span class="_ _f"> </span>basta<span class="_ _c"> </span>cono<span class="_ _9"></span>cer<span class="_ _c"> </span>la<span class="_ _f"> </span>longitud<span class="_ _c"> </span>de<span class="_ _f"> </span>dos<span class="_ _c"> </span>lados<span class="_ _f"> </span>o<span class="_ _c"> </span>la<span class="_ _f"> </span>amplitud<span class="_ _c"> </span>de<span class="_ _f"> </span>uno<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _f"> </span>´<span class="_ _d"></span>angulos</div><div class="t m0 xb h7 y33 ff6 fs3 fc0 sc0 ls0 ws0">agudos<span class="_ _21"> </span>y<span class="_ _21"> </span>la<span class="_ _21"> </span>longitud<span class="_ _21"> </span>de<span class="_ _21"> </span>uno<span class="_ _21"> </span>de<span class="_ _21"> </span>los<span class="_ _21"> </span>tres<span class="_ _21"> </span>lados<span class="_ _21"> </span>para<span class="_ _21"> </span>determinar<span class="_ _21"> </span>el<span class="_ _21"> </span>resto<span class="_ _21"> </span>de<span class="_ _21"> </span>los<span class="_ _21"> </span>cinco<span class="_ _21"> </span>elemen<span class="_ _12"></span>tos</div><div class="t m0 xb h7 y34 ff6 fs3 fc0 sc0 ls0 ws0">del<span class="_ _c"> </span>tri´<span class="_ _d"></span>angulo.</div><div class="t m0 x11 h9 y35 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x12 h9 y36 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1f h9 y37 ff8 fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x20 h9 y38 ff8 fs3 fc0 sc0 ls0 ws0">q</div><div class="t m0 x1f h9 y39 ff8 fs3 fc0 sc0 ls0 ws0">h</div><div class="t m0 x13 h9 y3a ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">α</span></div><div class="t m0 x14 h9 y3b ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">β</span></div><div class="t m0 x21 h9 y3c ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">ω</span></div><div class="t m0 x22 h9 y3d ff8 fs3 fc0 sc0 ls0 ws0"><span class="fc2 sc0">σ</span></div><div class="t m0 x15 h7 y3e ff6 fs3 fc0 sc0 ls0 ws0">3)<span class="_ _c"> </span><span class="ff5">Grup<span class="_ _9"></span>o<span class="_ _f"> </span>de<span class="_ _f"> </span>T<span class="_ _b"></span>eoremas<span class="_ _13"> </span>de<span class="_ _f"> </span>Pit´<span class="_ _14"></span>agoras</span></div><div class="t m0 x23 h7 y3f ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ff8">.</span>1)<span class="_ _22"> </span><span class="ff8">h</span></div><div class="t m0 x24 ha y40 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h7 y3f ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">p<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>q</span></div><div class="t m0 x23 h7 y41 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ff8">.</span>2)<span class="_ _22"> </span><span class="ff8">a</span></div><div class="t m0 x24 ha y42 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h7 y41 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>p</span></div><div class="t m0 x25 h9 y43 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x24 ha y44 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h7 y43 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>q</span></div><div class="t m0 x26 h7 y45 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ff8">.</span>3)<span class="_ _22"> </span><span class="ff8">c</span></div><div class="t m0 x24 ha y46 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h7 y45 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x27 ha y46 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x28 h7 y45 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x29 ha y46 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa h7 y47 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_"> </span>Es<span class="_ _e"> </span>suficiente<span class="_"> </span>cono<span class="_ _9"></span>cer<span class="_"> </span>la<span class="_ _e"> </span>longitud<span class="_ _20"> </span>de<span class="_ _e"> </span>dos<span class="_ _e"> </span>de<span class="_ _e"> </span>los<span class="_"> </span>seis<span class="_ _e"> </span>segmentos<span class="_"> </span>determinados,<span class="_ _e"> </span>o<span class="_ _20"> </span>uno<span class="_ _e"> </span>de</div><div class="t m0 xb h7 y48 ff6 fs3 fc0 sc0 ls0 ws0">ellos<span class="_ _c"> </span>y<span class="_ _c"> </span>uno<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _f"> </span>cuatro<span class="_ _e"> </span>´<span class="_ _a"></span>angulos<span class="_ _c"> </span>determinados<span class="_ _c"> </span>para<span class="_ _c"> </span>calcular<span class="_ _c"> </span>el<span class="_ _f"> </span>v<span class="_ _b"></span>alor<span class="_ _f"> </span>del<span class="_ _e"> </span>resto<span class="_ _f"> </span>de<span class="_ _e"> </span>los<span class="_ _f"> </span>diez</div><div class="t m0 xb h7 y49 ff6 fs3 fc0 sc0 ls0 ws0">elemen<span class="_ _3"></span>tos</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb h7 y9 ff5 fs3 fc0 sc0 ls0 ws0">Demostraci´<span class="_ _14"></span>on<span class="_ _f"> </span>de<span class="_ _f"> </span>3)</div><div class="t m0 xa h7 y4a ff6 fs3 fc0 sc0 ls0 ws0">Sean<span class="_ _c"> </span><span class="ffa">4</span></div><div class="t m0 x2a ha y4b ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2b h7 y4a ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ffa">4</span></div><div class="t m0 x2c ha y4b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2d h7 y4a ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ffa">4</span></div><div class="t m0 x2e ha y4b ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x2f h7 y4a ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>lados<span class="_ _c"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>h,<span class="_ _1f"> </span>p</span>),<span class="_ _c"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c</span>)<span class="_ _c"> </span>y<span class="_ _c"> </span>(<span class="ff8">b,<span class="_ _1f"> </span>h,<span class="_ _1f"> </span>q<span class="_ _9"></span></span>)<span class="_ _c"> </span>tenemos:</div><div class="t m0 x14 h7 y4c ffa fs3 fc0 sc0 ls0 ws0">4</div><div class="t m0 x30 ha y4d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x31 h7 y4c ffa fs3 fc0 sc0 ls0 ws0">∼<span class="_ _20"> </span>4</div><div class="t m0 x2c ha y4d ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x32 h7 y4c ff6 fs3 fc0 sc0 ls0 ws0">:</div><div class="t m0 x33 h9 y4e ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x33 h9 y4f ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x34 h7 y4c ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x3 h9 y4e ff8 fs3 fc0 sc0 ls0 ws0">h</div><div class="t m0 x35 h9 y4f ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x36 h7 y4c ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x37 h9 y4e ff8 fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x37 h9 y4f ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x38 h7 y4c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _21"> </span><span class="ff8">a</span></span></div><div class="t m0 x39 ha y50 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6 h7 y4c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>p</span></div><div class="t m0 x14 h7 y51 ffa fs3 fc0 sc0 ls0 ws0">4</div><div class="t m0 x30 ha y52 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x31 h7 y51 ffa fs3 fc0 sc0 ls0 ws0">∼<span class="_ _20"> </span>4</div><div class="t m0 x2c ha y52 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x32 h7 y51 ff6 fs3 fc0 sc0 ls0 ws0">:</div><div class="t m0 x33 h9 y53 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x33 h9 y54 ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x3a h7 y51 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2f h9 y53 ff8 fs3 fc0 sc0 ls0 ws0">h</div><div class="t m0 x2f h9 y54 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x3b h7 y51 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x10 h9 y53 ff8 fs3 fc0 sc0 ls0 ws0">q</div><div class="t m0 x10 h9 y54 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x3c h7 y51 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _21"> </span><span class="ff8">b</span></span></div><div class="t m0 x3d ha y55 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x5 h7 y51 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>q</span></div><div class="t m0 x3e hb y56 ffb fs3 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e hb y57 ffb fs3 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e hb y58 ffb fs3 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e hb y59 ffb fs3 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e hb y5a ffb fs3 fc0 sc0 ls0 ws0"></div><div class="t m0 x3f h7 y5b ff5 fs3 fc0 sc0 ls0 ws0">3.2)<span class="_ _f"> </span>T<span class="_ _b"></span>eorema<span class="_ _f"> </span>de<span class="_ _13"> </span>los<span class="_ _f"> </span>catetos</div><div class="t m0 x40 h7 y5c ffa fs3 fc0 sc0 ls0 ws0">4</div><div class="t m0 x41 ha y5d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x42 h7 y5c ffa fs3 fc0 sc0 ls0 ws0">∼<span class="_ _20"> </span>4</div><div class="t m0 x43 ha y5d ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x44 h7 y5c ff6 fs3 fc0 sc0 ls0 ws0">:</div><div class="t m0 x45 h9 y5e ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x45 h9 y5f ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x46 h7 y5c ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x47 h9 y5e ff8 fs3 fc0 sc0 ls0 ws0">h</div><div class="t m0 x47 h9 y5f ff8 fs3 fc0 sc0 ls0 ws0">q</div><div class="t m0 x13 h7 y5c ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x48 h9 y5e ff8 fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x48 h9 y5f ff8 fs3 fc0 sc0 ls0 ws0">h</div><div class="t m0 x49 h7 y5c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _21"> </span><span class="ff8">h</span></span></div><div class="t m0 x4a ha y60 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4b h7 y5c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">p<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>q<span class="_ _23"> </span><span class="ff5">3.1)<span class="_ _f"> </span>T<span class="_ _b"></span>eorema<span class="_ _f"> </span>de<span class="_ _13"> </span>la<span class="_ _f"> </span>altura</span></span></div><div class="t m0 xa h7 y61 ff6 fs3 fc0 sc0 ls0 ws0">Sumando<span class="_ _c"> </span>las<span class="_ _c"> </span>dos<span class="_ _c"> </span>ecuaciones<span class="_ _c"> </span>obtenidas<span class="_ _c"> </span>en<span class="_ _c"> </span>3<span class="ff8">.</span>2:</div><div class="t m0 x4c h9 y62 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x1 ha y63 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1f h7 y62 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x4d ha y63 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4e h7 y62 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>p<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>q</span></div><div class="t m0 x4e h7 y64 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c</span>(<span class="ff8">p<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">q<span class="_ _9"></span></span>)</div><div class="t m0 x4e h7 y65 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>c</span></div><div class="t m0 x4e h7 y66 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">c</span></div><div class="t m0 x4f ha y67 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x50 h7 y66 ff5 fs3 fc0 sc0 ls0 ws0">3.3)<span class="_ _f"> </span>T<span class="_ _b"></span>eorema<span class="_ _f"> </span>de<span class="_ _13"> </span>Pit´<span class="_ _14"></span>agoras</div><div class="t m0 xa h7 y68 ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _c"> </span>adem´<span class="_ _d"></span>as<span class="_ _c"> </span>que<span class="_ _f"> </span>el<span class="_ _e"> </span>´<span class="_ _a"></span>area<span class="_ _c"> </span>del<span class="_ _c"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _c"> </span>p<span class="_ _9"></span>o<span class="_ _24"></span>demos<span class="_ _c"> </span>expresarla<span class="_ _c"> </span>como:</div><div class="t m0 x51 h7 y69 ff8 fs3 fc0 sc0 ls0 ws0">A<span class="_ _20"> </span><span class="ff6">=</span></div><div class="t m0 x52 h9 y6a ff8 fs3 fc0 sc0 ls0 ws0">ab</div><div class="t m0 x3d h7 y6b ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x53 h7 y69 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">A<span class="_ _20"> </span></span>=</div><div class="t m0 x54 h9 y6a ff8 fs3 fc0 sc0 ls0 ws0">ch</div><div class="t m0 x55 h7 y6b ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x56 h7 y69 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _4"></span><span class="ffa">⇒</span></div><div class="t m0 x57 h9 y6a ff8 fs3 fc0 sc0 ls0 ws0">ab</div><div class="t m0 x58 h9 y6b ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x59 h7 y69 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">h</span></div><div class="t m0 xa h7 y6c ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _13"> </span>tam<span class="_ _12"></span>bi<span class="_ _3"></span>´<span class="_ _25"></span>en<span class="_ _13"> </span>que<span class="_ _13"> </span><span class="ff8">σ<span class="_ _8"> </span></span>=<span class="_ _13"> </span><span class="ff8">β<span class="_ _6"> </span></span>y<span class="_ _13"> </span><span class="ff8">ω<span class="_ _13"> </span></span>=<span class="_ _13"> </span><span class="ff8">α<span class="_ _8"> </span></span>p<span class="_ _24"></span>or<span class="_ _13"> </span>ser<span class="_ _13"> </span>´<span class="_ _d"></span>angulos<span class="_ _8"> </span>agudos<span class="_ _13"> </span>con<span class="_ _13"> </span>lados<span class="_ _13"> </span>resp<span class="_ _24"></span>ectiv<span class="_ _3"></span>amen<span class="_ _12"></span>te</div><div class="t m0 xb h7 y6d ff6 fs3 fc0 sc0 ls0 ws0">p<span class="_ _24"></span>erp<span class="_ _24"></span>endiculares</div><div class="t m0 xa h7 y6e ff6 fs3 fc0 sc0 ls0 ws0">4)</div><div class="t m0 x5a h9 y6f ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _26"> </span>B</div><div class="t m0 x1 h9 y70 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x5b h9 y71 ff8 fs3 fc0 sc0 ls0 ws0">M</div><div class="t m0 x5c h7 y72 ff6 fs3 fc0 sc0 ls0 ws0">Sea<span class="_ _c"> </span><span class="ff8">M<span class="_ _8"> </span></span>punto<span class="_ _e"> </span>medio<span class="_ _c"> </span>de<span class="_ _c"> </span><span class="ff8">AB</span></div><div class="t m0 x5c h7 y73 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _21"> </span><span class="ff8">AM<span class="_ _13"> </span><span class="ff6">=<span class="_"> </span></span>M<span class="_ _27"></span>B<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _27"></span>M</span></span></div><div class="t m0 x5d h7 y74 ff5 fs3 fc0 sc0 ls0 ws0">T<span class="_ _10"></span>eorema<span class="_ _13"> </span>de<span class="_ _f"> </span>la<span class="_ _13"> </span>mediana<span class="_ _f"> </span>de<span class="_ _13"> </span>la</div><div class="t m0 x1e h7 y75 ff5 fs3 fc0 sc0 ls0 ws0">hip<span class="_ _24"></span>oten<span class="_ _3"></span>usa</div><div class="t m0 xb h7 y76 ff5 fs3 fc0 sc0 ls0 ws0">Demostraci´<span class="_ _14"></span>on</div><div class="t m0 x5e h7 y77 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-)<span class="_ _16"> </span>Sea<span class="_ _c"> </span><span class="ff8">M<span class="_ _27"> </span>H<span class="_ _f"> </span></span></span>⊥<span class="_ _20"> </span><span class="ff8">C<span class="_ _28"></span>B<span class="_ _f"> </span><span class="ff6">en<span class="_ _c"> </span></span>H<span class="_ _f"> </span><span class="ff6">=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">M<span class="_ _27"></span>H<span class="_ _13"> </span><span class="ff6">es<span class="_ _c"> </span>la<span class="_ _c"> </span>paralela<span class="_ _c"> </span>media<span class="_ _c"> </span>de<span class="_ _c"> </span></span>AC</span></span></span></span></div><div class="t m0 x12 h7 y78 ffc fs3 fc0 sc0 ls0 ws0">∴<span class="_ _20"> </span><span class="ff8">M<span class="_ _27"></span>H<span class="_ _13"> </span><span class="ff6">es<span class="_ _c"> </span>altura<span class="_ _c"> </span>y<span class="_ _c"> </span>mediana<span class="_ _f"> </span>de<span class="_ _e"> </span></span>B<span class="_ _9"></span>C<span class="_ _13"> </span><span class="ff6">en<span class="_ _c"> </span><span class="ffa">4</span></span>C<span class="_ _28"></span>M<span class="_ _27"> </span>B</span></div><div class="t m0 x12 h7 y79 ff6 fs3 fc0 sc0 ls0 ws0">o<span class="_ _c"> </span>sea,<span class="_ _c"> </span><span class="ffa">4<span class="ff8">C<span class="_ _28"></span>M<span class="_ _27"></span>B<span class="_ _f"> </span></span></span>es<span class="_ _f"> </span>is´<span class="_ _d"></span>osceles<span class="_ _c"> </span>de<span class="_ _c"> </span>base<span class="_ _c"> </span><span class="ff8">C<span class="_ _28"></span>B<span class="_ _9"></span></span>,<span class="_ _c"> </span>etc...</div><div class="t m0 x5e h7 y7a ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-)<span class="_ _16"> </span>Sea<span class="_ _1e"> </span><span class="ff8">D<span class="_ _21"> </span></span>un<span class="_ _1e"> </span>punto<span class="_ _1e"> </span>de<span class="_ _1e"> </span>la<span class="_ _1e"> </span>prolongaci´<span class="_ _d"></span>on<span class="_ _1e"> </span>de<span class="_ _1e"> </span><span class="ff8">C<span class="_ _9"></span>M<span class="_ _29"> </span></span>;<span class="_ _1e"> </span><span class="ff8">C<span class="_ _9"></span>M<span class="_ _13"> </span></span>=<span class="_"> </span><span class="ff8">M<span class="_ _27"></span>D<span class="_ _e"> </span></span>=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _21"> </span><span class="ff8">AC<span class="_ _28"></span>B<span class="_ _9"></span>D<span class="_ _21"> </span><span class="ff6">es<span class="_ _1e"> </span>paralelogramo-</span></span></span></span></div><div class="t m0 x5f h7 y7b ff6 fs3 fc0 sc0 ls0 ws0">rect´<span class="_ _d"></span>angulo<span class="_ _c"> </span>y<span class="_ _c"> </span><span class="ff8">AM<span class="_ _13"> </span></span>=<span class="_"> </span><span class="ff8">M<span class="_ _27"> </span>B<span class="_ _c"> </span></span>=<span class="_"> </span><span class="ff8">C<span class="_ _28"></span>M<span class="_ _13"> </span></span>=<span class="_"> </span><span class="ff8">M<span class="_ _27"></span>D<span class="_ _c"> </span></span>p<span class="_ _9"></span>or<span class="_ _c"> </span>propiedades<span class="_ _c"> </span>de<span class="_ _c"> </span>un<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo</div><div class="t m0 x5e h7 y7c ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-)<span class="_ _16"> </span><span class="ff8">M<span class="_ _6"> </span></span>es<span class="_ _f"> </span>circuncen<span class="_ _3"></span>tro<span class="_ _f"> </span>del<span class="_ _f"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _13"> </span></span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _e"> </span><span class="ff8">AM<span class="_ _8"> </span><span class="ff6">=<span class="_ _c"> </span></span>M<span class="_ _27"></span>B<span class="_ _f"> </span><span class="ff6">=<span class="_ _c"> </span></span>M<span class="_ _27"></span>C<span class="_ _13"> </span><span class="ff6">=<span class="_ _f"> </span>radio<span class="_ _c"> </span>de<span class="_ _f"> </span>la<span class="_ _f"> </span>circunferencia</span></span></span></span></div><div class="t m0 x5f h7 y7d ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>cen<span class="_ _12"></span>tro<span class="_ _c"> </span><span class="ff8">M<span class="_ _8"> </span></span>que<span class="_ _c"> </span>pasa<span class="_ _f"> </span>por<span class="_ _c"> </span><span class="ff8">A</span>,<span class="_ _c"> </span><span class="ff8">B<span class="_ _13"> </span></span>y<span class="_ _c"> </span><span class="ff8">C<span class="_ _13"> </span></span>(rec<span class="_ _10"></span>´<span class="_ _11"></span>ıpro<span class="_ _24"></span>co<span class="_ _c"> </span>del<span class="_ _c"> </span>teorema<span class="_ _c"> </span>de<span class="_ _c"> </span>T<span class="_ _b"></span>ales)</div><div class="t m0 xb h7 y7e ff6 fs3 fc0 sc0 ls0 ws0">5)<span class="_ _c"> </span>En<span class="_ _c"> </span>to<span class="_ _24"></span>do<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _e"> </span>rect´<span class="_ _a"></span>angulo<span class="_ _c"> </span>con<span class="_ _c"> </span>un<span class="_ _c"> </span>´<span class="_ _a"></span>angulo<span class="_ _e"> </span>agudo<span class="_ _c"> </span>de<span class="_ _c"> </span>30</div><div class="t m0 x60 h8 y7f ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x16 h7 y7e ff6 fs3 fc0 sc0 ls0 ws0">tenemos:</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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L6LxWLPPvvsvffe+/rrr//kJz959NFHn3rqqRkzZoQQbr311rq6uu9973tHjhx54YUXcrncxo0bz9kPVltbu3///g0bNtTV1bW1tdmECQDA5yUyOjpqCvDJAyMyxqExNDS0d+/eWbNmXXvttSfedySEkMvlXn311UsvvTSZTEYikXP/A5dKpS1btjz00ENPPPHEqlWrotGoDxEAAG0J52Nbnv/KZ0337Nmzc+fOZDLpcwQAQFuCthynbDa7fv36q666asuWLdXV1T5NAADOAfstYaJJJpO9vb0rVqyYN29ee3u7TZgAAGhLYDyi0Wg6nR4eHh4cHKypqclkMmYCAMBZZU0sjHVgRCbOoZHL5VpaWgqFwo4dO2pra324AABoS9CW45TNZpuamlKpVEdHR1VVlY8YAIAzy5pYmBSSyWQ+n6+vr4/H4+3t7aVSyUwAANCWwCmLRqOtra3Dw8MHDhxIJBLd3d1mAgDAmWJNLIx1YEQm+KGRy+UaGxtDCLt27XKfEgAATp/zljAZVVdX79+/f8OGDXV1del02n1KAADQlsA4pdPpfD6/cOHCWCyWyWRswgQAQFsC4xGNRjdt2lQoFHbv3p1IJLLZrJkAADAO9lvCWAdGZDIeGtlsdv369fF4vKuryyZMAABOifOWwP+XTCZ7e3ubm5vr6ura2tpswgQAQFsC4xGNRtPpdH9/f2VlZU1NjU2YAACcJGtiYawDI+LQCLlcrqWlpVAobNu2LZlM+rcCAABtCdpynLLZbFNTUyqV6ujoqKqqMhAAAMZkTSzwaZLJZD6fX7FiRTweb29vt0QWAABtCYxHeRPm8PDwgQMHEolEJpMxEwAAPsHCPxjrwLAm9v+Qy+UaGxtDCLt27XKfEgAAtCVoy/Hr7u5et25dKpXq6uqqqKgwEAAArIkFTllDQ0M+n1+4cGEsFuvs7LQJEwAAbQmMRzQa3bRpU6FQ6OnpSSQS3d3dZgIAMJlZ+AdjHRjWxJ6Kvr6+tWvXxuPxrq4umzABACYn5y2B01VbW7t///7m5ua6urq2trZisWgmAADaEmA80ul0f39/ZWVlLBbLZDI2YQIAaEuA8aioqNi0adPAwMDu3buvueaabDZrJgAAk4RNZTDWgWG/5WnLZrNNTU2pVGrLli02YQIATHjOWwJnRTKZzOfzK1asmDdvXnt7uyWyAADaEmA8otFoOp0eHh4eHBxMJBKZTMZMAAAmKgv/YKwDw5rYMy2Xy7W0tBQKhR07dtTW1hoIAIC2BG3JOHV3d69bty6VSnV0dFRVVRkIAMCEYU0scO40NDTk8/n6+vp4PN7Z2WkTJgCAtgQYj2g02traOjw83NPTk0gkuru7zQQAYAKw8A/GOjCsiT0n+vr61q5dG0LYtWuX+5QAAFzQnLcEPje1tbX79+/fsGFDXV1dW1tbsVg0EwAAbQkwHul0Op/PV1ZWxmKxTCZjEyYAgLYEGI9oNLpp06aBgYHdu3cnEolsNmsmAAAXFpvKYKwDw37Lz082m12/fn08Hu/q6rIJEwDgQuG8JXB+SSaTvb29zc3NdXV17e3tNmECAGhLgPGIRqPpdLq/v39wcLCmpsYmTACA85+FfzDWgWFN7Hkjl8u1tLQUCoUdO3bU1tYaCACAtgRtyThls9mmpqZUKtXR0VFVVWUgAADnG2tigQtAMpnM5/P19fXxeLy9vd0SWQAAbQkwHtFotLW1dXh4+MCBA4lEoru720wAAM4fFv7BWAeGNbHnt1wu19jYGELYtWuX+5QAAJwPnLcELjzV1dX79+/fsGFDXV1dOp12nxIAAG0JME7pdDqfzy9cuDAWi3V2dtqECQCgLQHGIxqNbtq0qVAo9PT0JBKJbDZrJgAAnwubymCsA8N+ywtQX1/f2rVr4/F4V1eXTZgAAOeY85bABFFbW9vb29vc3FxXV9fW1mYTJgCAtgQYj2g0mk6n+/v7Kysra2pqMpmMTZgAAOeGhX8w1oFhTeyFL5fLtbS0FAqFbdu2JZNJAwEA0JagLRmnbDbb1NSUSqU6OjqqqqoMBADgLLEmFpjIkslkPp9fsWJFPB5vb2+3RBYAQFsCjEd5E+bw8PDg4GAikchkMmYCAHDGWfgHYx0Y1sROULlcrrGxMYSwY8eO2tpaAwEA0JagLRmn7u7udevWpVKprq6uiooKA4EL8bf0p7/A73CAc8+aWGDSaWhoyOfz9fX1sViss7PTJky44Ix+FiMC0JYA50I0Gm1tbS0UCj09PYlEoru720wAAE6HhX8w1oFhTexk0tfXt3bt2ng83tXVVV1dbSAAAOPgvCUw2dXW1u7fv7+5ubmurq6tra1YLJoJAMCpcnIGxjownLecKF5++eW+vr6hoaGvfOUrjY2NU6b84Q/Udu/effDgwS984QvXXnvtF7/4xRBCsVj87ne/u3nz5htuuGHRokX333//pZdeaoYAACfDeUv4P/PyJJnVees73/lOCOHv//7v77///kceeWTlypXH/8hg48aNv/rVr+66667bbrvtgQce2LNnTwihoqLio48+evHFF+Px+DPPPNPc3OwyPwAA2hJOy+jJMajz+RPcvHnzk08+WY7Gr3/967t27XrjjTdCCG+++eb27dvvvvvuEMK0adM2bNhw1113lf+ujz/+ePny5ZlM5tlnn33zzTdvueWWXC5nmAAA2hKYpCKRyIMPPrh69eryw/IuylgsFkJ4/vnnv/SlL02dOrX8pQULFrz99tsHDhwIIYyMjJSfTCaTf/M3f3PzzTfPmzevvb3dJkwAAG0JTFL333//smXLQgijo6M/+MEPmpuby5eB3bt378yZM4+/bNasWSGEV155JYSwbNmyBx988Be/+MVjjz129OjRe+65Z3h4eHBwsKamJpPJGCkAgLYEJqPf/va3Tz/99Jo1a26//fbt27eXnxwaGjqxLadMmTJz5swPPvgghNDU1JROp1977bX58+dv2bIlhFBRUdHR0bFv377HH3988eLFfX19pgoA8MeiRgBMYDNnzkwmkxdffPHmzZurqqpWrlwZQjhy5Mj06dNPfNm0adOOr3pdtGjRokWLPvF9qqur//M//7O7u3vZsmWpVKqjo6Oqqsp4AQCOc94SmMimT59+2WWXLVu27O67725qaspmsyGEWbNmHTt27MSXDQ8Pl7difrqGhoZ8Pl9fXx+Pxzs7O11FFgBAWwITXPluIkePHi0/XLJkyejo6GOPPRZCuOSSSw4fPnz8lUeOHDl27Fg8Hj+ZbxuNRltbW4eHh3t6ehKJRHd3t1EDAGhLYMJ6/PHHb7755ueff778sHyicsqUKSGE5cuXv//++8df+eGHH4YQUqnUyX/zioqKTCbz0ksvPfDAA4sXL3afEgAAbQlMTPPnz7/++uu/+tWvlh/29vaGEMq3JLn11lv7+/vLSRlC6OnpWbp0aSKRONW3qK2t3b9//4YNG+rq6tLptPuUAADaEmCiWb58eSqV+rd/+7ef//zn//Vf/9Xe3t7R0XHTTTeFEC655JJHHnmkra1tcHDwv//7vx999NHjl5Adh3Q6nc/nFy5cGIvFMpmMTZgAwOQUGR0dNQX45IEROdlD4+Rfyefi4MGDP/vZz6ZNm7ZkyZJP7KgcGhp65ZVXpkyZcuONN86YMeP03+vQoUNtbW179uzZuXNnMpk0fABAW4K21JaMUzabXb9+fTwe7+rqqq6uNhAAYJKwJhbgTEomk729vc3NzXV1de3t7TZhAgCThFMuMNaBEYkYAmfE3Xff3dnZaQ4AwIQXNQIYkzWxjFupVHrmmWfWrFnzz//8zxs3bjQQAEBbAnBqstlsU1NTKpUqFApVVVUGAgBMEk65wFgHhmv5TBQvv/xyX1/f0NDQV77ylcbGxilT/rDJfPfu3QcPHvzCF75w7bXXfvGLXyw/+fHHHz/88MO//vWvp0+fft9991166aWn9HalUunmm2/+p3/6J9eJBQC0JaAtJ4jvfOc7f/7nf37jjTcWi8W/+qu/mjlz5nPPPVfeTLtx48Y/+ZM/ueeee44ePfrXf/3Xra2tqVQqhPCP//iPt99+e21t7dDQ0N/93d/9+7//ezRqfQdMkF/sn/4Cv8wBTpPrxAIT0+jo6ObNm5988skQQkVFxde//vVdu3a98cYbIYQ333xz+/btd999dwhh2rRpGzZsuOuuu8p/18cff1xbWxtCmD179vXXX9/X12eSMGF+J3w6IwLQlnDmPfHEE4ZwoYtEIg8++ODq1avLD8v3AonFYiGE559//ktf+tLUqVPLX1qwYMHbb7994MCBEMLIyMjx7/DrX/969uzZn/IW2Wx28eLF7jICABBcywfGlE6nDWECuP/++8t/MTo6+oMf/KC5ubm6ujqEsHfv3pkzZx5/2axZs0IIr7zyysKFC5ctW/bggw+uXLny5z//+cjIyJ/+6Z+O+Z0PHTrU1ta2Z8+enTt3VlRUGDUAgPOWwET229/+9umnn16zZs3tt9++ffv28pNDQ0MntuWUKVNmzpz5wQcfhBCamprS6fRrr702f/78LVu2/PE3LJVK7e3t8Xh8xYoV+XzeNXsAAMqctwQmspkzZyaTyYsvvnjz5s1VVVUrV64MIRw5cmT69OknvmzatGnHl7YuWrRo0aJF/9c3fPXVVw8cODA8POx0JQCAtgQmi+nTp1922WWXXXbZ0NBQU1PT3r17k8nkrFmzjh07duLLhoeHy1sxP1MymXSuEgDgj1kTC0xMH3300Ysvvnj06NHywyVLloyOjj722GMhhEsuueTw4cPHX3nkyJFjx47F43FDAwDQlnAmfeZt0Dj/Pf744zfffPPzzz9fflg+UTllypQQwvLly99///3jr/zwww9DCOX7W56oVCp1dnYuXrzYMAEAtCUwSc2fP//666//6le/Wn7Y29sbQijfkuTWW2/t7+8vJ2UIoaenZ+nSpYlE4sS/vbu7O5FI9PT0vPzyy4YJAPCZIm4WDGMcGKdy3tJBdN5qb2+fNm3a8uXL//d//3f9+vV/+7d/e88995S/9NRTT7344otbt2597733/uEf/mHbtm01NTXlL+VyuZaWlkKhsGPHjtraWmMEANCWMP62dGhMDAcPHvzZz342bdq0JUuWfGJH5dDQ0CuvvDJlypQbb7xxxowZx59va2v7i7/4C/c4BQDQlqAtAQDgnLLfEgAAAG0JZ8HAwIAhTAa5XC6dTnd3dxsFAIC2hDOvurraECa2UqnU3t4+b968FStWLFu2zEAAALQlwKnJZDKJRGJwcHB4eDidTkejUTMBADhN/o8KmFyKxeLu3bv37dvn7DQAwBnkYpgAAACcLmtiAQAA0JZwFkQiEUOYGLq7u+fOnVssFo0CAOCsst8SmJhyuVxjY2MI4aWXXqqoqDAQAICzynlLYKIpFottbW11dXUbNmzYv39/bW2tmQAAnG3OWwITza9+9avKysp8Pu/mIgAA54zrxMJYB0bEoQEAAKfAmlgAAAC0JZwFAwMDhnBBKBaL7e3t6XTaKAAAtCWcd6qrqw3hPFcqlTKZTE1NzeDgYFdXl4EAAHy+XOgCuPD09fWtXbs2Ho/v27fPHwQAAGhLgPF47rnntm3blkwmjQIA4DzhYpgAAACcLvstAQAA0JZwFkQiEUM4T+RyucWLF3d3dxsFAIC2BDhlxWIxnU7X1dVt2LChoaHBQAAAtCXAKSiVSp2dnbFYbOHChfl83u0rAQDOf64TC5x3RkZG3n777UKhUFVVZRoAABcE14mFsQ6MiEMDAABOgTWxAAAAaEs4CwYGBgzh3CiVSplMZu7cuaVSyTQAAC5c9lvCGKqrqw3hHMhms+vXr4/H4/v27YtG/ToCANCWAKfi0KFDbW1te/bs2blzZzKZNBAAgAudC5YAn4NsNvvuu++uWrXK6UoAAG0JAAAAIbiWD3BuuFQPAIC2hEknEokYwplSLBbT6fS3vvUtowAA0JYAp6xUKnV2dsZisfr6+q1btxoIAMAE5ioawFnR3d29bt26VCpVKBSqqqoMBFvFOEgAACAASURBVABAWwKcstdff/2ll16qra01CgCAycB1YmGsAyPi0AAAgFNgvyVwBrgMLACAtgQ+aWBgwBBOXjabTSQS2WzWKAAAJi0L/4Dxy+VyGzdufOONN7Zt25ZMJg0EAGDSct4SGI9SqdTe3j5v3rwVK1b09vYKSwCASc51YoHxGBkZCSEMDw9XVFSYBgAA1sQCAABwuqyJBU6KK8ECAKAt4dREIhFDOLEqOzs7p02bJi8BANCWwHh0d3cnEomenp7h4eFo1A5tAADG5v8UgbHlcrnGxsYQwksvvVRbW2sgAAB8CtfygbEOjIhDI2Sz2XfffTedTvv3AQAAbQnaEgAAzjr7LYH/r1gsGgIAANoSzpiBgYFJ9c+by+VuuummrVu3+ugBABgfC/9gUisWi1u3bn3kkUe2bt26atUqV4IFAGB8nLeEySuTydTU1AwODvb396fTaWEJAMC4+V9JmLyGhob27dtXXV1tFAAAnCZrYgEAADhd1sTCZFEqlQwBAABtCedOJBKZYP9EmUwmkUj09fX5cAEAOBvst4QJLpfLNTY2hhBsrQQAQFsCp6xYLLa0tOzZs+exxx5raGgwEAAAtCUwHgsXLvyP//gPNxcBAOBsc51YGOvAiDg0AADgFLiWD0wcxWLREAAA+FxYKQdjGBgYGPP5H/7wh++8886xY8dWrVo1d+7c8pMjIyNPPPHE1KlTp06d2tDQMHv27PLzBw8efPjhh0dGRubOnXvffffNmDHjrFblxo0bn3nmmffee8/HBwDAuee8JYzhj6+nWiwW77jjjmKx2Nra2tDQcNttt5WfL5VKt9xyy5e//OU77rjjhhtuaGxsLBQK5ecfeOCBhx566JFHHvna1762cePGs/SjlkqlTCYTi8UqKyv7+/t9dgAAaEs4f917770LFixoamoKIfzoRz966623fv/734cQtm/fPmvWrCVLloQQ5s6de8stt3z7298OIfzyl79cunTpxRdfHEK4+uqrP/roo7PxU/X19V1zzTW7d+8eGBjYtGlTRUWFTwoAgM+FNbHw2d56663vf//7//M//1N+2Nraeuedd06ZMiWE8Nxzz9XV1R1/5YIFC/71X/91dHR09uzZJy5PHRkZORs/WD6f37ZtWzKZ9BkBAKAt4Xz3wgsvzJkzZ86cOU8//fTUqVOvu+66qqqq8pf27t17ww03HH/lrFmzfvOb37zzzjs1NTVHjx7dvn37n/3Znz377LPLly8/Gz+Yu1YCAHCesCYWPtuBAwdmz569ffv2VCqVSqWam5t//OMfhxB+97vfFYvFmTNnntiWIYQPPvgghLB58+b58+e/9tpr6XR69erVZ+QncSVYAAC0JVwwIpHIiQ8HBgb6+/tvuummeDxeWVn5zW9+8xvf+Mbhw4ePHDkSQpg+ffrxV06bNu3EArzuuuvuvPPORYsWnf6P1NfXt3jx4q1bt/p0AAA4D1kTC5/toosumjNnzhVXXFF+eNVVV7333ns//elP//Iv/zKEcOzYseOvPHz4cAghFoudwXcvFostLS179ux57LHHLIIFAOD85LwlfLbLL7/8xEuwlk9U5nK5aDRaWVlZ7skT2zIej5+pt+7s7IzFYvX19fl8XlgCAHDect4SPlt9ff2TTz55/GH5hiILFiwIISxfvvz9998//qUPP/zwiiuuuPzyy8/UWw8NDRUKheOXDgIAgPOT85bw2VauXHnRRRe9+eab5Yevv/76lVdeuXTp0hDC6tWr9+7de/yVPT09a9asOYNvvWnTJmEJAIC2hIkgFos9++yz99577+uvv/6Tn/zk0Ucffeqpp2bMmBFCuPXWW+vq6r73ve8dOXLkhRdeyOVyGzduHPcbuQwsAAAXqMjo6KgpwMkYGhrau3fvrFmzrr322hPvOxJCyOVyr7766qWXXppMJj9xjdmTVCqVnnnmmTVr1gwMDFRXV5s2AADaEjg12Wy2qakplUpt2bJFWAIAcCFyLR/4PB06dKitre2NN97YuXNnMpk0EAAALlDOW8LnqVgs7tq1a9WqVdGoP+gBAEBbAgAAMIm5TiycU64ECwCAtoTJYnzXev10hw4dSqfT9fX1xgsAgLYETlmpVGpvb4/H4/X19b29vQYCAMDE4/IhcHYdv7/I8PBwRUWFgQAAoC2BU/bhhx/u27fPXSsBAJjYXCcWxjowIg4NAAA4BfZbwplUKpVcCRYAAG0JhBDC+E5aZrPZRCLx+OOPGyAAAJON/ZZwBuRyuZaWlkKhsHPnzmQyaSAAAEw2zlvCaSmVSm1tbXV1dc3Nzb29vcISAIDJyXlLOL1DKBq98sor+/v73V8EAIDJzMUwAQAAOF3WxMKpcRlYAADQlnBSIpHIHz9ZKpXa29tjsdihQ4eMCAAAtCWcskwmk0gkDhw4MDw8XFVVZSAAAHAi1/KBz3Do0KEbb7wxhLBv377q6moDAQCAP+ZaPjDWgRH5w6Fx6NCh1157raGhwVgAAEBbwjjbEgAA+Ez2WwIAAHC6nJwBAADgdDlvCQAAgLYEAABAWwIAAKAtAQAA0JYAAACgLQEAANCWAAAAaEsAAAC0JQAAAGhLAAAAtCUAAADaEgAAAG0JAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWAAAAoC0BAADQlgAAAGhLAAAAtCUAAABoSwAAALQlAAAA2hIAAABtCQAAANoSAAAAbQkAAIC2BAAAQFsCAACAtgQAAEBbAgAAoC0BAADQlgAAAKAtAQAA0JYAAABoSwAAALQlAAAAaEsAAAC0JQAAANoSAAAAbQkAAADaEgAAAG0JAACAtgQAAEBbAgAAgLYEAABAWwIAAKAtAQAA0JYAAACgLQEAANCWAAAAaEsAAAC0JQAAAGhLAAAAtCUAAADaEgAAAG0JAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWAAAAoC0BAADQlgAAAGhLAOAzFYvFyGcxJeAc/LYxIsYnMjo6agoAAACcDuctAQAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAPy/9u4fRKprgeP4PXAnLOx2YWzUxDF2YhNJYZfAFv5LhHRZ/xRil377lDaBbQUVNuwGUghGWUUhpAlJETeBNClEV0mVaXdAkgvzCh/79i3+Obtz7p375/PpnMId7nhcv+/8sg/QlgAAAGhLAAAAtCUAAABoSwAAALQlAAAA2hIAAABtCQAAANoSAAAAbQkAAIC2BAAAQFsCAACAtgQAAEBbAgAAoC0BAADQlgAAAKAtAQAA0JYAAABoSwAAALQlAAAAaEsAAAC0JQAAANoSAAAAbQkAAADaEgAAAG0JAACAtgQAAEBbAgAAgLYEAABAWwIAAKAtAQAA0JYAAACgLQEAANCWAAAAaEsAAAC0JQAAAGhLAAAAtCUAAADaEgAAAG0JAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWAAAAoC0BAADQlgAAAGhLAAAAtCUAAABoSwAAALQlAAAA2hIAAABtCQAAANoSAAAAbQkAAIC2BAAAQFsCAACAtgQAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAAC0JQAAAGhLAAAAtCUAAADaEgAAAG0JAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWwOutr69vbGx4DgAAoC1h744fPz4YDFZXVz0KAAB4pTAejz0FeMs5CeHvv/+en58/evTo8vJynueeCQCw/Z8KFXyVyH+3V/Nm4t8P3eHeEqL0+/1Hjx71+/2DBw/axwIAOyqrArV6M8KSV/zvGv5YwNvPSfjfSVlbWztz5szKysrCwoInAwAA2hL20pZZlg2HQ/tYAADYziYWds0+FgAAdnBvCRHnJLz6pNjHAgCAtoRJ2zKzjwUAgCzLbGJhQvaxAACQubeEqHMS3n5S7GMBANCWwKRtmdnHAgDQYTaxkIx9LAAAneXeEiLOSdjdSbGPBQBAWwKTtmVmHwsAQMfYxEIp7GMBAOgU95YQcU7C3k+KfSwAANoSmLQtM/tYAAA6wCYWSmcfCwBA67m3hIhzEtKcFPtYAAC0JWjLBOxjAQBoJZtYqJR9LAAAreTeEiLOSUh/UuxjAQDQlqAtE7CPBQCgNWxiYWrsYwEAaA33lhBxTkK5J8U+FgAAbQnaMgH7WAAAGs0mFmrBPhYAgEZzbwkR5yRUd1LsYwEA0JagLROwj4V2K4qi1+uV/VV8fwegYjaxUDv2sdBueZ6Py+c5A1Ax95YQcU7CdE6KfSwAANoStGUC9rEAADSCTSzUmn0sAACN4N4SIs5JmP5JsY8FAEBbgrZMwD4WAIDasomFxrCPBQCgttxbQsQ5CfU6KfaxAABoS9CWCdjHAgBQKzax0Ej2sQAA1Ip7S4g4J6G+J8U+FgAAbQnaMgH7WAAAps4mFhrPPhYAgKlzbwkR5yQ046TYxwIAoC1BWyZgHwsAwFTYxEKr2McCADAV7i0h4pyE5p0U+1gAALQlaMsE7GMBAKiMTSy0ln0sAACVcW8JEeckNPuk2McCAKAtQVsmYB8LAECpbGKhE+xjAQAolXtLiDgnoT0nxT4WAABtCdoyAftYAACSs4mFzrGPBQAgOfeWEHFOQjtPin0sAADaErRlAvaxAAAkYRMLnWYfCwBAEu4tIeKchPafFPtYAAC0JWjLBOxjAQDYM5tY4L/sYwEA2DP3lhBxTkK3Top9LAAA2hK0ZQL2sQAA7IpNLPAK9rEAAOyKe0uIOCehuyfFPhYAAG0J2jKBHfvY4XB49+7ds2fP9vt9fzYAAHjJJhZ4i6197IEDBz788MMDBw5cvnz5vffeO3HiRFEUng8AANoSiJLn+dLS0oULF3777bd//vkny7IXL1788ssv3377rYcDAEBmEwtR5yQ4KVmWZYcPH3769On2VwaDwZMnTzwZAADcWwIAAKAtgap89dVXO175/PPPPRYAALQlsAtffPHFZ599tvXLkydPPnjwYGFhwU/0AQBAWwKx8jy/ffv25ubmysrK5ubmvXv31tfX+/3+wYMHNzY2PB8AgC7zE0og4pz4WT5vtLa2dubMmZWVlYWFBU8DAEBbAtpyj4bD4fz8/NGjR5eXl/M890AAALrGJhZIoN/vP3r0yD4WAKCz3MZAxDlxbxnNPhYAQFsC2jIB+1gAgA6yiQUSs48FAOggtzEQcU7cW+6JfSwAgLYEtGUC9rEAAB1hEwuUyD4WGmo0GoXyeecAbeI2BiLOiXvLidnHAgBoS9CWTkoC9rEAAC1mEwtUxD4WAKDF3MZAxDlxb5mUfSwAgLYEbUkC9rEAAC1jEwtMgX0sAEDLuI2BiHPi3rI09rEAANoStCUJ2McCALSATSwwZfaxAAAt4DYGIs6Je8tK2McCAGhL0JYkYB8LANBQNrFAjdjHAgA0lNsYiDgn7i0rZx8LAKAtQVuSgH0sAECD2MQCNWUfCwDQIG5jIOKcuLecKvtYAABtCdqSBOxjAQBqziYWaAD7WACAmnMbAxHnxL1lbdjHAgBoS9CWJGAfCwBQQzaxQMPYxwIA1JDbGIg4J+4ta8k+FgBAW4K2JAH7WACAmrCJBRrMPhYAoCbcxkDEOXFvWXv2sQAA2hK0JQnYxwIATJFNLNAS9rEAAFPkNgYizol7y0axjwUA0JZQ07b8999/GzGzHA6H/X7fR2YfCwBQMZtYeJM//vjj9OnTWZa9++67X3/9dVEUtX2rd+7cOXz48L59+44cOXLnzp2Of3D2sQAAFXNvCa9VFEWv19v+yuLi4tWrV2v4Vn/66aePP/54K33zPF9fXz927JgP0T4WAEBbwpR98803ly5d2vFiPcexH3300a+//rr9lVOnTq2trfkQM/tYAIBK2MTCa/3www87XnnnnXf++uuvGr7VHWGZZdnPP//sE3zJPhYAQFvCNF25cmVmZmb7K/v37z906FAN3+ri4uKOV7788kuf4JY8z5eWlq5fvz4YDFZXVz0QAIDkbGLhTY4cOfLs2bOX/x3jzMzMtWvXLl68WMP3ubGxMRgMtr+yubk5OzvrE9zBPhYAoCTuLeFN/vzzzx9//DHLssXFxefPn9czLLMsO3To0Obm5o0bN+bn55eXl4Xl69jHAgCUxL0lRJyT4KS0jZ8fCwCgLUFbkoB9LABAQjaxQEfZxwIAJOQ2BiLOiXvLVrOPBQDQlqAtScA+FgBgQjaxAPaxAACTchsDEefEvWVn2McCAGhL0JYkYB8LALAHNrEA/8c+FgBgD9zGQMQ5cW/ZSfaxAADaErQlCdjHAgBEsokFeC37WACASG5jIOKcuLfsPPtYAABtCdqSBOxjAQDewCYWIIp9LADAG7iNgYhz4t6SbexjAQC0JWhLErCPpfVGo9Hc3FzZX6Wkv1pDCNU8Jd8aALaziQXYNftYWm92dnZcvvKSrxr+nABs5zYGIs6Je0tewz4WAEBbgrYkAftYAIDMJhZgQvaxAACZe0uIOifuLYlgHwsAaEtAW5KAfSwA0Fk2sQDJ2McCAJ3lNgYizol7S3bJPhYA0JaAtiQB+1gAoFNsYgFKYR8LAHSK2xiIOCfuLZmAfSwAoC0BbUkC9rEAQOvZxAKUzj4WAGg9tzEQcU7cW5KIfSwAoC1BW0IC9rEAQCvZxAJUyj4WAGgltzEQcU7cW1IC+1gAQFuCtoQE7GMBgNawiQWYGvtYAKA13MZAxDlxb0nJ7GMBAG0J2hISsI8FABrNJhagFuxjAYBGcxsDEefEvSUVso8FALQlaEtIwD4WAGgcm1iA2rGPBQAax20MRJwT95ZMiX0sAKAtQVtCAvaxAEAj2MQC1Jp9LADQCG5jIOKcuLekBuxjAQBtCdoSErCPBQBqyyYWoDHsYwGA2nIbAxHnxL0lNWMfCwBoS9CWZRkOhw8fPjx37tzs7KxPrfXsYwGAWrGJhTYYjUanT5/et2/f+fPn5+bmzp07VxSFx9Ju9rEAgLYEErt169a9e/e2fvngwYPtv6St8jxfWlq6fv36YDBYXV31QACAKbKJhYhzUvtN7Pvvv//8+fPtr3zwwQePHz/22XXE1j5WYQIA2hLqqyiKXq/nOVB//koHALQlsHc3b968fPny1i9nZma+++67Tz/91JMBAEBbArFGo9H8/Pzvv//+4sWLmZmZTz755Pvvv/ezQwEA0JbArg2Hw/v37588ebLf73saAABoSwAAAJrE/wcJAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWAAAAoC0BAADQlgAAADRZ7hEAADuMRqO5ubkKvtB4PC7jtw0hVPOgSnr/AE0U/J0IAADAhGxiAQAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAAHib3CMAqEZRFL1er4IvNB6P0/6GIYRqHlHydw4AVCb4Rg4AAMCEbGIBAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAVC33CACqURRFr9cr+6uMx+OEv9toNJqbm6vg4aR92wBA9YJv5wAAAEzIJhYAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAgN3KPQKAahRF0ev1yv4q4/E47W8YQqjm+SR/5wBAlYLv5QAAAEzIJhYAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAlCH3CAAqFkKo1fsZj8c+FABg0n/h+CcFAAAAE7KJBQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABAWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAANCWAAAAaEsAAAC0JQAAANoSAAAAtCUAAADaEgAAAG0JAACAtgQAAABtCQAAgLYEAABA7A4FPAAAAcJJREFUWwIAAKAtAQAAQFsCAACgLQEAANCWAAAAaEsAAADQlgAAAGhLAAAAtCUAAADaEgAAALQlAAAA2hIAAABtCQAAgLYEAAAAbQkAAIC2BAAAQFsCAACgLQEAAEBbAgAAoC0BAADQlgAAAGhLAAAA0JYAAABoSwAAALQlAAAA2hIAAAC0JQAAANoSAAAAbQkAAIC2BAAAAG0JAACAtgQAAEBbAgAAoC0BAABAWwIAAKAtAQAA0JYAAABoSwAAALQlAAAAaEsAAAC0JQAAANoSAAAAbQkAAADaEgAAAG0JAACAtgQAAEBbAgAAgLYEAABAWwIAAKAtAQAA0JYAAACgLQEAANCWAAAAaEsAAAC0JQAAAGhLAAAAtCUAAADaEgAAAG0JAAAA2hIAAABtCQAAgLYEAABAWwIAAIC2BAAAQFsCAACgLQEAANCWAAAAoC0BAADQlgAAAGhLAAAAtCUAAABoSwAAALQlAAAA2hIAAABtCQAAANoSAAAAbQkAAIC2BAAAQFsCAACAtgQAAEBbAgAAoC0BAADQlgAAAKAtAQAA0JYAAABoSwAAALQlAAAAaEsAAAAqEELwEAAAAJjUfwDllmP/PHLcyAAAAABJRU5ErkJggg=="/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 x61 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">i)<span class="_ _16"> </span>El<span class="_ _f"> </span>cateto<span class="_ _13"> </span>opuesto<span class="_ _f"> </span>al<span class="_ _13"> </span>´<span class="_ _d"></span>angulo<span class="_ _13"> </span>de<span class="_ _f"> </span>30</div><div class="t m0 x62 h8 y80 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x63 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">mide<span class="_ _f"> </span>la<span class="_ _13"> </span>longitud<span class="_ _13"> </span>de<span class="_ _f"> </span>la<span class="_ _13"> </span>hipotenusa<span class="_ _f"> </span>dividida<span class="_ _13"> </span>p<span class="_ _24"></span>or</div><div class="t m0 x5f h7 y81 ff6 fs3 fc0 sc0 ls0 ws0">dos<span class="_ _c"> </span>(<span class="ff8">a<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">c<span class="_ _1e"> </span><span class="ffa">÷<span class="_ _1e"> </span></span></span>2)</div><div class="t m0 x64 h7 y82 ff6 fs3 fc0 sc0 ls0 ws0">ii)<span class="_ _16"> </span>El<span class="_ _c"> </span>cateto<span class="_ _f"> </span>adyacen<span class="_ _3"></span>te<span class="_ _f"> </span>al<span class="_ _f"> </span>´<span class="_ _a"></span>angulo<span class="_ _f"> </span>de<span class="_ _c"> </span>30</div><div class="t m0 x63 h8 y83 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x3e h7 y82 ff6 fs3 fc0 sc0 ls0 ws0">mide</div><div class="t m0 x65 h7 y84 ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x66 h7 y82 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="_ _f"> </span>v<span class="_ _3"></span>eces<span class="_ _f"> </span>la<span class="_ _f"> </span>longitud<span class="_ _f"> </span>del<span class="_ _f"> </span>cateto<span class="_ _f"> </span>opuesto</div><div class="t m0 x5f h7 y85 ff6 fs3 fc0 sc0 ls0 ws0">al<span class="_ _c"> </span>´<span class="_ _d"></span>angulo<span class="_ _c"> </span>de<span class="_ _f"> </span>30</div><div class="t m0 x46 h8 y86 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x67 h7 y85 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">b<span class="_ _20"> </span></span>=</div><div class="t m0 x68 h7 y87 ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x51 h7 y85 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ff8">a</span>)</div><div class="t m0 xb h7 y88 ff5 fs3 fc0 sc0 ls0 ws0">Demostraci´<span class="_ _14"></span>on</div><div class="t m0 x11 h9 y89 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x11 h9 y8a ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x69 h9 y8b ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x69 h9 y8c ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x69 h9 y8d ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x21 hc y8e ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc2 sc0">60</span></div><div class="t m0 x1 hd y8f ff7 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">◦</span></div><div class="t m0 x21 hc y90 ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc2 sc0">60</span></div><div class="t m0 x1 hd y91 ff7 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">◦</span></div><div class="t m0 x6a hc y92 ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc2 sc0">30</span></div><div class="t m0 x6b hd y93 ff7 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">◦</span></div><div class="t m0 x6a hc y94 ff6 fs5 fc0 sc0 ls0 ws0"><span class="fc2 sc0">30</span></div><div class="t m0 x6b hd y95 ff7 fs6 fc0 sc0 ls0 ws0"><span class="fc2 sc0">◦</span></div><div class="t m0 x15 h7 y96 ff6 fs3 fc0 sc0 ls0 ws0">Reflejando<span class="_ _1e"> </span>el<span class="_ _1e"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _1e"> </span>dado<span class="_ _1e"> </span>de<span class="_ _1e"> </span>lados<span class="_ _1e"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c</span>)</div><div class="t m0 x15 h7 y97 ff6 fs3 fc0 sc0 ls0 ws0">sobre<span class="_ _2b"> </span>el<span class="_ _2b"> </span>cateto<span class="_ _2b"> </span><span class="ff8">b<span class="_ _2b"> </span></span>obtengo<span class="_ _2b"> </span>un<span class="_ _2b"> </span>tri´<span class="_ _d"></span>angulo</div><div class="t m0 x15 h7 y98 ff6 fs3 fc0 sc0 ls0 ws0">equil´<span class="_ _d"></span>atero</div><div class="t m0 x15 h7 y99 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _c"> </span><span class="ff6">i)<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span></span>=</span></span></div><div class="t m0 x6c h9 y9a ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x6c h7 y9b ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6d h7 y9c ff6 fs3 fc0 sc0 ls0 ws0">ii)<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span></span>=</div><div class="t m0 x26 h7 y9d ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x6e h7 y9c ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ff8">a<span class="_ _c"> </span></span>(p<span class="_ _24"></span>or<span class="_ _c"> </span>T<span class="_ _b"></span>eo.<span class="_ _c"> </span>de<span class="_ _c"> </span>Pit´<span class="_ _a"></span>agoras)</div><div class="t m0 x15 h7 y9e ff6 fs3 fc0 sc0 ls0 ws0">nota:<span class="_ _c"> </span>De<span class="_ _c"> </span>aqu<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _f"> </span>se<span class="_ _c"> </span>obtienen<span class="_ _c"> </span>las<span class="_ _f"> </span>razones<span class="_ _e"> </span>trigo-</div><div class="t m0 x15 h7 y9f ff6 fs3 fc0 sc0 ls0 ws0">nom<span class="_ _3"></span>´<span class="_ _25"></span>etricas<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>´<span class="_ _a"></span>angulos<span class="_ _e"> </span>30</div><div class="t m0 x28 h8 ya0 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x6f h7 y9f ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span>60</div><div class="t m0 x70 h8 ya0 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 xb h7 ya1 ff6 fs3 fc0 sc0 ls0 ws0">6)<span class="_ _c"> </span>En<span class="_ _c"> </span>to<span class="_ _24"></span>do<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _e"> </span>rect´<span class="_ _a"></span>angulo<span class="_ _c"> </span>e<span class="_ _c"> </span>is´<span class="_ _d"></span>osceles<span class="_ _f"> </span>tenemos:</div><div class="t m0 x5f h7 ya2 ff6 fs3 fc0 sc0 ls0 ws0">La<span class="_"> </span>longitud<span class="_"> </span>de<span class="_"> </span>la<span class="_ _20"> </span>hip<span class="_ _24"></span>otenusa<span class="_"> </span>es<span class="_"> </span>igual<span class="_"> </span>a</div><div class="t m0 x71 h7 ya3 ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x72 h7 ya2 ff6 fs3 fc0 sc0 ls0 ws0">2<span class="_"> </span>veces<span class="_"> </span>la<span class="_"> </span>longitud<span class="_"> </span>de<span class="_"> </span>los<span class="_"> </span>catetos<span class="_"> </span>(<span class="ff8">c<span class="_ _20"> </span></span>=</div><div class="t m0 x73 h7 ya3 ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x74 h7 ya2 ff6 fs3 fc0 sc0 ls0 ws0">2<span class="ff8">s</span>)</div><div class="t m0 x5f h7 ya4 ff6 fs3 fc0 sc0 ls0 ws0">Esto<span class="_ _c"> </span>es<span class="_ _c"> </span>resultado<span class="_ _c"> </span>de<span class="_ _c"> </span>aplicar<span class="_ _c"> </span>teorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Pit´<span class="_ _a"></span>agoras<span class="_ _c"> </span>con<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">b</span></div><div class="t m0 x5f h7 ya5 ff6 fs3 fc0 sc0 ls0 ws0">nota:<span class="_ _c"> </span>de<span class="_ _c"> </span>aqu<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>se<span class="_ _c"> </span>obtienen<span class="_ _c"> </span>las<span class="_ _c"> </span>razones<span class="_ _c"> </span>trigonom´<span class="_ _a"></span>etricas<span class="_ _c"> </span>del<span class="_ _c"> </span>´<span class="_ _d"></span>angulo<span class="_ _f"> </span>de<span class="_ _e"> </span>45</div><div class="t m0 x75 h8 ya6 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 xb h7 ya7 ff5 fs3 fc0 sc0 ls0 ws0">*<span class="_ _f"> </span><span class="ff6">7)<span class="_ _c"> </span>En<span class="_ _f"> </span>to<span class="_ _24"></span>do<span class="_ _f"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _c"> </span>rect´<span class="_ _a"></span>angulo,<span class="_ _f"> </span>la<span class="_ _c"> </span>suma<span class="_ _f"> </span>de<span class="_ _f"> </span>la<span class="_ _f"> </span>longitud<span class="_ _f"> </span>del<span class="_ _f"> </span>inradio<span class="_ _c"> </span>y<span class="_ _f"> </span>el<span class="_ _f"> </span>circunradio<span class="_ _f"> </span>es</span></div><div class="t m0 xb h7 ya8 ff6 fs3 fc0 sc0 ls0 ws0">igual<span class="_ _c"> </span>a<span class="_ _c"> </span>la<span class="_ _c"> </span>media<span class="_ _c"> </span>aritm´<span class="_ _a"></span>etica<span class="_ _e"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>catetos.</div><div class="t m0 xb h7 ya9 ff5 fs3 fc0 sc0 ls0 ws0">Demostraci´<span class="_ _14"></span>on</div><div class="t m0 x11 h9 yaa ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _26"> </span>B</div><div class="t m0 x76 h9 yab ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x2c h9 yac ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x2b h9 yad ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x11 h9 yae ff8 fs3 fc0 sc0 ls0 ws0">R<span class="_ _2c"> </span>O</div><div class="t m0 x77 h9 yaf ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x78 h9 yb0 ff8 fs3 fc0 sc0 ls0 ws0">r</div><div class="t m0 x30 h9 yb1 ff8 fs3 fc0 sc0 ls0 ws0">r<span class="_ _2d"> </span>y</div><div class="t m0 x2f h9 yb2 ff8 fs3 fc0 sc0 ls0 ws0">y</div><div class="t m0 x31 h9 yb3 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x15 h7 yb4 ff6 fs3 fc0 sc0 ls0 ws0">Sean<span class="_ _1b"> </span><span class="ff8">P<span class="_ _1f"> </span></span>,<span class="_ _1b"> </span><span class="ff8">Q</span>,<span class="_ _2e"> </span><span class="ff8">R<span class="_ _2e"> </span></span>pun<span class="_ _3"></span>tos<span class="_ _2e"> </span>de<span class="_ _1b"> </span>tangencia<span class="_ _2e"> </span>del</div><div class="t m0 x15 h7 yb5 ff6 fs3 fc0 sc0 ls0 ws0">inc<span class="_ _10"></span>´<span class="_ _11"></span>ırculo<span class="_ _e"> </span>del<span class="_ _e"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _13"> </span></span></span>con<span class="_ _20"> </span>los<span class="_ _c"> </span>lados<span class="_ _e"> </span><span class="ff8">AB<span class="_ _9"></span></span>,<span class="_ _e"> </span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _28"></span></span>,</div><div class="t m0 x15 h7 yb6 ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _9"></span>A<span class="ff6">,<span class="_ _f"> </span>tenemos:</span></div><div class="t m0 x66 h7 yb7 ff8 fs3 fc0 sc0 ls0 ws0">AR<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>AP<span class="_ _13"> </span><span class="ff6">=<span class="_"> </span></span>x</div><div class="t m0 x66 h7 yb8 ff8 fs3 fc0 sc0 ls0 ws0">RC<span class="_ _f"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _9"></span>Q<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>r<span class="_ _f"> </span><span class="ff6">(inradio)</span></div><div class="t m0 x66 h7 yb9 ff8 fs3 fc0 sc0 ls0 ws0">P<span class="_ _29"> </span>B<span class="_ _c"> </span><span class="ff6">=<span class="_"> </span></span>QB<span class="_ _c"> </span><span class="ff6">=<span class="_"> </span></span>y</div><div class="t m0 x79 h7 yba ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _9"></span>Q<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>QB<span class="_ _c"> </span><span class="ff6">=<span class="_"> </span></span>r<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>y</span></span></div><div class="t m0 x35 h7 ybb ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>AR<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>RC<span class="_ _f"> </span><span class="ff6">=<span class="_"> </span></span>x<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>r</div><div class="t m0 x35 h7 ybc ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>AP<span class="_ _f"> </span><span class="ff6">+<span class="_ _1e"> </span></span>P<span class="_ _29"> </span>B<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>x<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>y<span class="_ _c"> </span><span class="ff6">=<span class="_"> </span>di´<span class="_ _d"></span>ametro<span class="_ _f"> </span>del<span class="_ _e"> </span>circunc<span class="_ _10"></span>´<span class="_ _11"></span>ırculo</span></div><div class="t m0 x4e h7 ybd ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>r<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>y<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>x<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>r<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span>2</span>R<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span>2</span>r</span></span></div><div class="t m0 x7a h7 ybe ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">r<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>R<span class="_ _20"> </span><span class="ff6">=</span></span></span></div><div class="t m0 x68 h7 ybf ff8 fs3 fc0 sc0 ls0 ws0">a<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b</div><div class="t m0 x51 h7 yc0 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa h7 y49 ff6 fs3 fc0 sc0 ls0 ws0">8)<span class="_ _c"> </span>,<span class="_ _c"> </span>9).<span class="_ _c"> </span>10),<span class="_ _c"> </span>...<span class="_ _c"> </span>pueden<span class="_ _c"> </span>ser<span class="_ _c"> </span>sugerencias<span class="_ _f"> </span>de<span class="_ _e"> </span>los<span class="_ _c"> </span>lectores<span class="_ _f"> </span>a<span class="_ _e"> </span>este<span class="_ _c"> </span>humilde<span class="_ _e"> </span>traba<span class="_ _9"></span>jo.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">4</div><div class="t m0 xb h5 yc1 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#2<span class="_ _6"> </span>-<span class="_ _16"> </span>Rectas<span class="_ _6"> </span>y<span class="_ _16"> </span>Pun<span class="_ _3"></span>tos<span class="_ _6"> </span>Notables</div><div class="t m0 xa h7 yc2 ff6 fs3 fc0 sc0 ls0 ws0">Presta<span class="_ _f"> </span>m<span class="_ _3"></span>ucha<span class="_ _f"> </span>atenci´<span class="_ _d"></span>on<span class="_ _f"> </span>a<span class="_ _f"> </span>estas<span class="_ _f"> </span>notas,<span class="_ _f"> </span>de<span class="_ _f"> </span>seguro<span class="_ _f"> </span>aprender´<span class="_ _a"></span>as<span class="_ _f"> </span>cosas<span class="_ _f"> </span>m<span class="_ _3"></span>uy<span class="_ _f"> </span>nov<span class="_ _3"></span>edosas<span class="_ _f"> </span>que</div><div class="t m0 xb h7 yc3 ff6 fs3 fc0 sc0 ls0 ws0">servir´<span class="_ _d"></span>an<span class="_ _c"> </span>para<span class="_ _c"> </span>elev<span class="_ _3"></span>ar<span class="_ _c"> </span>tu<span class="_ _c"> </span>cultura<span class="_ _f"> </span>matem´<span class="_ _d"></span>atica.</div><div class="t m0 xa h7 yc4 ff6 fs3 fc0 sc0 ls0 ws0">i)<span class="_ _8"> </span>En<span class="_ _13"> </span>to<span class="_ _24"></span>do<span class="_ _8"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _13"> </span>hay<span class="_ _13"> </span>para<span class="_ _8"> </span>cada<span class="_ _8"> </span>lado<span class="_ _8"> </span>una<span class="_ _8"> </span>altura,<span class="_ _8"> </span>una<span class="_ _8"> </span>mediana,<span class="_ _13"> </span>una<span class="_ _8"> </span>mediatriz<span class="_ _8"> </span>y</div><div class="t m0 xb h7 yc5 ff6 fs3 fc0 sc0 ls0 ws0">para<span class="_ _c"> </span>cada<span class="_ _c"> </span>´<span class="_ _a"></span>angulo<span class="_ _e"> </span>una<span class="_ _f"> </span>bisectriz.<span class="_ _e"> </span>cada<span class="_ _c"> </span>una<span class="_ _f"> </span>de<span class="_ _e"> </span>estas<span class="_ _f"> </span>rectas<span class="_ _e"> </span>concurren<span class="_ _c"> </span>en<span class="_ _f"> </span>un<span class="_ _e"> </span>punto<span class="_ _e"> </span>llamado:</div><div class="t m0 xb h7 yc6 ff6 fs3 fc0 sc0 ls0 ws0">orto<span class="_ _24"></span>cen<span class="_ _3"></span>tro,<span class="_ _f"> </span>baricen<span class="_ _3"></span>tro,<span class="_ _c"> </span>circuncentro<span class="_ _e"> </span>e<span class="_ _c"> </span>incentro<span class="_ _e"> </span>(<span class="ff8">H<span class="_ _24"></span>,<span class="_ _1f"> </span>G,<span class="_ _1f"> </span>T<span class="_ _28"></span>,<span class="_ _1f"> </span>I<span class="_ _27"></span></span>)</div><div class="t m0 xa h7 yc7 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-<span class="_ _f"> </span>alturas</span></div><div class="t m0 x7b h9 yc8 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 yc9 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x7c h9 yca ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x7d h9 ycb ff8 fs3 fc0 sc0 ls0 ws0">H</div><div class="t m0 x7e h7 ycc ff6 fs3 fc0 sc0 ls0 ws0">Segmen<span class="_ _3"></span>tos<span class="_ _c"> </span>que<span class="_ _f"> </span>“parten”<span class="_ _e"> </span>de<span class="_ _c"> </span>cada<span class="_ _c"> </span>v´<span class="_ _a"></span>ertice<span class="_ _c"> </span>y<span class="_ _c"> </span>“caen”<span class="_ _c"> </span>p<span class="_ _24"></span>erp<span class="_ _24"></span>en-</div><div class="t m0 x7e h7 ycd ff6 fs3 fc0 sc0 ls0 ws0">dicularmen<span class="_ _3"></span>te<span class="_ _6"> </span>en<span class="_ _8"> </span>los<span class="_ _6"> </span>lados<span class="_ _8"> </span>opuestos.<span class="_ _6"> </span>V<span class="_ _10"></span>emos<span class="_ _6"> </span>que<span class="_ _8"> </span><span class="ff8">H<span class="_ _2f"> </span></span>es<span class="_ _8"> </span>un</div><div class="t m0 x7e h7 yce ff6 fs3 fc0 sc0 ls0 ws0">pin<span class="_ _3"></span>to<span class="_ _e"> </span>interior<span class="_"> </span>del<span class="_ _e"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _e"> </span>si<span class="_ _e"> </span>este<span class="_ _20"> </span>es<span class="_ _e"> </span>acut´<span class="_ _a"></span>angulo,<span class="_"> </span>p<span class="_ _24"></span>ero<span class="_ _e"> </span>si<span class="_ _e"> </span>es</div><div class="t m0 x7e h7 ycf ff6 fs3 fc0 sc0 ls0 ws0">un<span class="_ _e"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _e"> </span>obtus´<span class="_ _d"></span>angulo<span class="_ _c"> </span>en<span class="_ _12"></span>tonces<span class="_ _e"> </span><span class="ff8">H<span class="_ _13"> </span></span>es<span class="_ _e"> </span>un<span class="_ _c"> </span>punto<span class="_"> </span>exterior</div><div class="t m0 x7e h7 yd0 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _f"> </span>si<span class="_ _f"> </span>el<span class="_ _f"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _f"> </span>es<span class="_ _f"> </span>rect´<span class="_ _a"></span>angulo<span class="_ _f"> </span>en<span class="_ _12"></span>tonces<span class="_ _f"> </span><span class="ff8">H<span class="_ _6"> </span></span>coincide<span class="_ _f"> </span>con<span class="_ _f"> </span>el</div><div class="t m0 x7e h7 yd1 ff6 fs3 fc0 sc0 ls0 ws0">v<span class="_ _3"></span>´<span class="_ _25"></span>ertice<span class="_ _c"> </span>del<span class="_ _c"> </span>´<span class="_ _d"></span>angulo<span class="_ _f"> </span>recto</div><div class="t m0 xa h7 yd2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-<span class="_ _f"> </span>medianas</span></div><div class="t m0 x7b h9 yd3 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 yd4 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x7c h9 yd5 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x4d h9 yd6 ff8 fs3 fc0 sc0 ls0 ws0">G</div><div class="t m0 x7f h9 yd7 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x80 h9 yd8 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x81 h9 yd9 ff8 fs3 fc0 sc0 ls0 ws0">R</div><div class="t m0 x7e h7 yda ff6 fs3 fc0 sc0 ls0 ws0">Segmen<span class="_ _3"></span>tos<span class="_ _6"> </span>que<span class="_ _6"> </span>“parten”<span class="_ _6"> </span>de<span class="_ _6"> </span>cada<span class="_ _6"> </span>v´<span class="_ _a"></span>ertice<span class="_ _6"> </span>y<span class="_ _6"> </span>“caen”<span class="_ _6"> </span>en<span class="_ _6"> </span>el</div><div class="t m0 x7e h7 ydb ff6 fs3 fc0 sc0 ls0 ws0">pun<span class="_ _3"></span>to<span class="_ _f"> </span>medio<span class="_ _f"> </span>de<span class="_ _c"> </span>cada<span class="_ _f"> </span>lado.<span class="_ _f"> </span>V<span class="_ _10"></span>emos<span class="_ _f"> </span>que<span class="_ _f"> </span><span class="ff8">G<span class="_ _c"> </span></span>siempre<span class="_ _f"> </span>v<span class="_ _3"></span>a<span class="_ _c"> </span>a<span class="_ _f"> </span>ser</div><div class="t m0 x7e h7 ydc ff6 fs3 fc0 sc0 ls0 ws0">un<span class="_ _c"> </span>pun<span class="_ _12"></span>to<span class="_ _c"> </span>in<span class="_ _12"></span>terior<span class="_ _c"> </span>del<span class="_ _c"> </span>tri´<span class="_ _d"></span>angulo</div><div class="t m0 x82 h7 ydd ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span><span class="ff8">AG<span class="_ _21"> </span></span>=<span class="_"> </span>2<span class="ff8">GP<span class="_ _1f"> </span></span>,<span class="_ _e"> </span><span class="ff8">B<span class="_ _9"></span>G<span class="_ _20"> </span></span>=<span class="_"> </span>2<span class="ff8">GQ</span>,<span class="_ _c"> </span><span class="ff8">C<span class="_ _28"></span>G<span class="_ _20"> </span></span>=<span class="_"> </span>2<span class="ff8">GR</span></div><div class="t m0 x83 h7 yde ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">P<span class="_ _27"> </span>Q</span>,<span class="_ _f"> </span><span class="ff8">QR<span class="_ _c"> </span></span>y<span class="_ _f"> </span><span class="ff8">RP<span class="_ _6"> </span></span>son<span class="_ _f"> </span>las<span class="_ _c"> </span>paralelas<span class="_ _f"> </span>medias<span class="_ _c"> </span>de<span class="_ _c"> </span><span class="ff8">AB<span class="_ _9"></span></span>,<span class="_ _f"> </span><span class="ff8">B<span class="_ _24"></span>C</span></div><div class="t m0 x84 h7 ydf ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">C<span class="_ _28"></span>A<span class="_ _c"> </span></span>resp<span class="_ _24"></span>ectiv<span class="_ _3"></span>amen<span class="_ _3"></span>te</div><div class="t m0 x82 h7 ye0 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Los<span class="_ _30"> </span><span class="ffa">4<span class="ff8">AGR</span></span>,<span class="_ _30"> </span><span class="ffa">4<span class="ff8">B<span class="_ _9"></span>GR<span class="_ _24"></span></span></span>,<span class="_ _30"> </span><span class="ffa">4<span class="ff8">B<span class="_ _9"></span>GP<span class="_ _29"> </span></span></span>,<span class="_ _2"> </span><span class="ffa">4<span class="ff8">C<span class="_ _28"></span>GP<span class="_ _29"> </span></span></span>,<span class="_ _30"> </span><span class="ffa">4<span class="ff8">C<span class="_ _28"></span>GQ<span class="_ _2"> </span></span></span>y</div><div class="t m0 x84 h7 ye1 ffa fs3 fc0 sc0 ls0 ws0">4<span class="ff8">AGQ<span class="_ _c"> </span><span class="ff6">tienen<span class="_ _c"> </span>la<span class="_ _c"> </span>misma<span class="_ _c"> </span>´<span class="_ _a"></span>area</span></span></div><div class="t m0 xa h7 ye2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-<span class="_ _f"> </span>mediatrices</span></div><div class="t m0 x7b h9 ye3 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 ye4 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x7c h9 ye5 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x42 h9 ye6 ff8 fs3 fc0 sc0 ls0 ws0">T</div><div class="t m0 x7f h9 ye7 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x80 h9 ye8 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x85 h9 ye9 ff8 fs3 fc0 sc0 ls0 ws0">R</div><div class="t m0 x7e h7 yea ff6 fs3 fc0 sc0 ls0 ws0">Rectas<span class="_"> </span>p<span class="_ _24"></span>erp<span class="_ _24"></span>endiculares<span class="_"> </span>a<span class="_"> </span>cada<span class="_"> </span>lado<span class="_"> </span>que<span class="_"> </span>pasan<span class="_"> </span>por<span class="_"> </span>el<span class="_"> </span>punto</div><div class="t m0 x7e h7 yeb ff6 fs3 fc0 sc0 ls0 ws0">medio<span class="_ _e"> </span>de<span class="_ _c"> </span>cada<span class="_ _c"> </span>lado.<span class="_ _c"> </span>V<span class="_ _b"></span>emos<span class="_ _e"> </span>que<span class="_ _c"> </span><span class="ff8">T<span class="_ _6"> </span></span>es<span class="_ _e"> </span>un<span class="_ _c"> </span>punto<span class="_ _e"> </span>in<span class="_ _3"></span>terior<span class="_ _c"> </span>del</div><div class="t m0 x7e h7 yec ff6 fs3 fc0 sc0 ls0 ws0">tri´<span class="_ _d"></span>angulo<span class="_ _f"> </span>si<span class="_ _c"> </span>este<span class="_ _f"> </span>es<span class="_ _c"> </span>acut´<span class="_ _d"></span>angulo,<span class="_ _f"> </span>p<span class="_ _24"></span>ero<span class="_ _c"> </span>si<span class="_ _f"> </span>es<span class="_ _c"> </span>obtus´<span class="_ _d"></span>angulo<span class="_ _f"> </span>en-</div><div class="t m0 x7e h7 yed ff6 fs3 fc0 sc0 ls0 ws0">tonces<span class="_ _21"> </span><span class="ff8">T<span class="_ _13"> </span></span>es<span class="_ _21"> </span>un<span class="_ _21"> </span>pun<span class="_ _12"></span>to<span class="_ _21"> </span>exterior<span class="_"> </span>y<span class="_ _1e"> </span>si<span class="_"> </span>el<span class="_ _1e"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _21"> </span>es<span class="_ _21"> </span>rect´<span class="_ _d"></span>angulo</div><div class="t m0 x7e h7 yee ff6 fs3 fc0 sc0 ls0 ws0">en<span class="_ _3"></span>tonces<span class="_ _f"> </span><span class="ff8">T<span class="_ _6"> </span></span>coincide<span class="_ _e"> </span>con<span class="_ _c"> </span>el<span class="_ _c"> </span>punto<span class="_ _e"> </span>medio<span class="_ _c"> </span>de<span class="_ _f"> </span>la<span class="_ _e"> </span>hip<span class="_ _24"></span>otenusa</div><div class="t m0 x7f h7 yef ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">T<span class="_ _6"> </span></span>coincide<span class="_ _e"> </span>con<span class="_ _c"> </span>el<span class="_ _c"> </span>centro<span class="_ _e"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>circunferencia<span class="_ _f"> </span>circunscrita<span class="_ _e"> </span>al<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo</div><div class="t m0 x7f h7 yf0 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">GH<span class="_ _c"> </span></span>=<span class="_"> </span>2<span class="ff8">GT<span class="_ _6"> </span></span>(recuerda<span class="_ _c"> </span>que<span class="_ _c"> </span><span class="ff8">G<span class="_ _c"> </span></span>es<span class="_ _f"> </span>el<span class="_ _e"> </span>baricentro<span class="_ _e"> </span>y<span class="_ _c"> </span><span class="ff8">H<span class="_ _8"> </span></span>el<span class="_ _c"> </span>orto<span class="_ _24"></span>centro)</div><div class="t m0 x7f h7 yf1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Los<span class="_ _e"> </span>puntos<span class="_ _e"> </span><span class="ff8">H<span class="_ _28"></span></span>,<span class="_ _c"> </span><span class="ff8">G</span>,<span class="_ _f"> </span><span class="ff8">T<span class="_ _6"> </span></span>son<span class="_ _e"> </span>alineados<span class="_ _c"> </span>(Recta<span class="_ _c"> </span>de<span class="_ _c"> </span>Euler)</div><div class="t m0 x7f h7 yf2 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>T<span class="_ _10"></span>o<span class="_ _24"></span>do<span class="_ _f"> </span>pun<span class="_ _3"></span>to<span class="_ _f"> </span>situado<span class="_ _c"> </span>en<span class="_ _f"> </span>la<span class="_ _f"> </span>mediatriz<span class="_ _c"> </span>de<span class="_ _f"> </span>cualquier<span class="_ _c"> </span>lado<span class="_ _f"> </span>equidista<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _f"> </span>extremos<span class="_ _c"> </span>del</div><div class="t m0 x5f h7 yf3 ff6 fs3 fc0 sc0 ls0 ws0">lado</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">5</div><div class="t m0 xa h7 y9 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _27"></span><span class="ff6">-<span class="_ _f"> </span>bisectrices</span></div><div class="t m0 x7b h9 yf4 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 yf5 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x7c h9 yf6 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x86 h9 yf7 ff8 fs3 fc0 sc0 ls0 ws0">I</div><div class="t m0 x87 h9 yf8 ff8 fs3 fc0 sc0 ls0 ws0">Z</div><div class="t m0 x88 h9 yf9 ff8 fs3 fc0 sc0 ls0 ws0">Y</div><div class="t m0 x4d h9 yfa ff8 fs3 fc0 sc0 ls0 ws0">X</div><div class="t m0 x7d h9 yfb ff8 fs3 fc0 sc0 ls0 ws0">k</div><div class="t m0 x7c h9 yfc ff8 fs3 fc0 sc0 ls0 ws0">k</div><div class="t m0 x89 h9 yfd ff8 fs3 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8a h9 yfe ff8 fs3 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8b h9 yff ff8 fs3 fc0 sc0 ls0 ws0">m</div><div class="t m0 x45 h9 y100 ff8 fs3 fc0 sc0 ls0 ws0">m</div><div class="t m0 x7e h7 y101 ff6 fs3 fc0 sc0 ls0 ws0">Son<span class="_ _c"> </span>rectas<span class="_ _c"> </span>que<span class="_ _c"> </span>dividen<span class="_ _f"> </span>a<span class="_ _c"> </span>cada<span class="_ _c"> </span>´<span class="_ _a"></span>angulo<span class="_ _e"> </span>del<span class="_ _f"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _c"> </span>en<span class="_ _c"> </span>dos</div><div class="t m0 x7e h7 y102 ff6 fs3 fc0 sc0 ls0 ws0">´<span class="_ _d"></span>angulos<span class="_ _13"> </span>de<span class="_ _13"> </span>igual<span class="_ _13"> </span>amplitud.<span class="_ _13"> </span>v<span class="_ _3"></span>emos<span class="_ _13"> </span>que<span class="_ _13"> </span><span class="ff8">I<span class="_ _6"> </span></span>siempre<span class="_ _13"> </span>v<span class="_ _3"></span>a<span class="_ _f"> </span>a<span class="_ _13"> </span>ser</div><div class="t m0 x7e h7 y103 ff6 fs3 fc0 sc0 ls0 ws0">un<span class="_ _c"> </span>pun<span class="_ _12"></span>to<span class="_ _c"> </span>in<span class="_ _12"></span>terior<span class="_ _c"> </span>del<span class="_ _c"> </span>tri´<span class="_ _d"></span>angulo</div><div class="t m0 x82 h7 y104 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span><span class="ff8">I<span class="_ _8"> </span></span>coincide<span class="_ _f"> </span>con<span class="_ _c"> </span>el<span class="_ _f"> </span>centro<span class="_ _c"> </span>de<span class="_ _f"> </span>la<span class="_ _c"> </span>circunferencia<span class="_ _f"> </span>inscrita</div><div class="t m0 x84 h7 y105 ff6 fs3 fc0 sc0 ls0 ws0">en<span class="_ _c"> </span>el<span class="_ _c"> </span>tri´<span class="_ _d"></span>angulo</div><div class="t m0 x82 h7 y106 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span><span class="ff8">C<span class="_ _9"></span>X</span></div><div class="t m0 x63 ha y107 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x8c h7 y106 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">AC<span class="_ _1e"> </span><span class="ffa">·<span class="_ _29"></span></span>C<span class="_ _28"></span>B<span class="_ _1e"> </span><span class="ffa">−<span class="_ _29"></span></span>AX<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1f"></span></span>X<span class="_ _28"></span>B<span class="_ _9"></span></span>,<span class="_"> </span>an´<span class="_ _a"></span>alogamen<span class="_ _3"></span>te<span class="_ _e"> </span>para<span class="_ _e"> </span><span class="ff8">AY</span></div><div class="t m0 x84 h7 y108 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">B<span class="_ _9"></span>Z</span></div><div class="t m0 x82 h7 y109 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span><span class="ff8">AI<span class="_ _6"> </span></span>:<span class="_ _13"> </span><span class="ff8">B<span class="_ _9"></span>I<span class="_ _16"> </span></span>=<span class="_ _13"> </span><span class="ff8">AX<span class="_ _16"> </span></span>:<span class="_ _13"> </span><span class="ff8">B<span class="_ _9"></span>X<span class="_ _28"></span></span>,<span class="_ _8"> </span><span class="ff8">B<span class="_ _9"></span>I<span class="_ _6"> </span></span>:<span class="_ _8"> </span><span class="ff8">C<span class="_ _28"></span>I<span class="_ _6"> </span></span>=<span class="_ _8"> </span><span class="ff8">B<span class="_ _9"></span>Y<span class="_"> </span></span>:<span class="_ _13"> </span><span class="ff8">C<span class="_ _28"></span>Y<span class="_ _1e"> </span></span>,<span class="_ _13"> </span><span class="ff8">C<span class="_ _28"></span>I<span class="_ _16"> </span></span>:</div><div class="t m0 x84 h7 y10a ff8 fs3 fc0 sc0 ls0 ws0">AI<span class="_ _f"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _9"></span>Z<span class="_ _f"> </span><span class="ff6">:<span class="_"> </span></span>AZ</div><div class="t m0 x82 h7 y10b ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>T<span class="_ _10"></span>o<span class="_ _24"></span>do<span class="_"> </span>pun<span class="_ _3"></span>to<span class="_"> </span>situado<span class="_"> </span>en<span class="_ _21"> </span>la<span class="_"> </span>bisetriz<span class="_ _21"> </span>de<span class="_"> </span>cualquier<span class="_ _21"> </span>´<span class="_ _d"></span>angulo</div><div class="t m0 x84 h7 y10c ff6 fs3 fc0 sc0 ls0 ws0">equidista<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="_ _c"> </span>que<span class="_ _c"> </span>determinan<span class="_ _c"> </span>al<span class="_ _c"> </span>´<span class="_ _a"></span>angulo</div><div class="t m0 xb h7 y10d ff6 fs3 fc0 sc0 ls0 ws0">2)<span class="_ _c"> </span>P<span class="_ _12"></span>articularidades<span class="_ _c"> </span>imp<span class="_ _24"></span>ortan<span class="_ _12"></span>tes</div><div class="t m0 xa h7 y10e ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _13"> </span>que<span class="_ _8"> </span>los<span class="_ _13"> </span>cuatro<span class="_ _8"> </span>putos<span class="_ _13"> </span>y<span class="_ _8"> </span>4<span class="_ _8"> </span>rectas<span class="_ _13"> </span>notables<span class="_ _8"> </span>no<span class="_ _13"> </span>tienen<span class="_ _8"> </span>p<span class="_ _24"></span>orqu´<span class="_ _d"></span>e<span class="_ _8"> </span>coincidir<span class="_ _8"> </span>p<span class="_ _24"></span>ero<span class="_ _13"> </span>en<span class="_ _8"> </span>un</div><div class="t m0 xb h7 y10f ff6 fs3 fc0 sc0 ls0 ws0">tri´<span class="_ _d"></span>angulo<span class="_ _f"> </span>is´<span class="_ _d"></span>osceles,<span class="_ _f"> </span>las<span class="_ _c"> </span>4<span class="_ _f"> </span>rectas<span class="_ _c"> </span>notables<span class="_ _f"> </span>referidas<span class="_ _c"> </span>a<span class="_ _f"> </span>las<span class="_ _c"> </span>base<span class="_ _f"> </span>coinciden<span class="_ _c"> </span>y<span class="_ _f"> </span>los<span class="_ _c"> </span>cuatro<span class="_ _f"> </span>pin<span class="_ _3"></span>tos</div><div class="t m0 xb h7 y110 ff6 fs3 fc0 sc0 ls0 ws0">notables<span class="_ _c"> </span>ser<span class="_ _10"></span>´<span class="_ _11"></span>ıan<span class="_ _c"> </span>pun<span class="_ _12"></span>tos<span class="_ _c"> </span>alineados<span class="_ _c"> </span>sobre<span class="_ _c"> </span>ellas.</div><div class="t m0 xa h7 y111 ff6 fs3 fc0 sc0 ls0 ws0">Ahora<span class="_ _13"> </span>el<span class="_ _13"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _13"> </span>equil´<span class="_ _a"></span>atero<span class="_ _f"> </span>“esconde”<span class="_ _13"> </span>otras<span class="_ _13"> </span>“cositas”<span class="_ _13"> </span>que<span class="_ _13"> </span>hacen<span class="_ _13"> </span>de<span class="_ _f"> </span>´<span class="_ _a"></span>el<span class="_ _13"> </span>un<span class="_ _13"> </span>p<span class="_ _24"></span>ol<span class="_ _10"></span>´<span class="_ _11"></span>ıgono</div><div class="t m0 xb h7 y112 ff6 fs3 fc0 sc0 ls0 ws0">m<span class="_ _3"></span>uy<span class="_ _f"> </span>in<span class="_ _3"></span>teresante,<span class="_ _e"> </span>veamos...</div><div class="t m0 x7f h7 y113 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>P<span class="_ _3"></span>ara<span class="_ _c"> </span>cada<span class="_ _c"> </span>lado<span class="_ _c"> </span>las<span class="_ _c"> </span>cuatro<span class="_ _f"> </span>rectas<span class="_ _e"> </span>notables<span class="_ _c"> </span>coinciden</div><div class="t m0 x7f h7 y114 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Los<span class="_ _e"> </span>cuatro<span class="_ _c"> </span>pntos<span class="_ _e"> </span>notables<span class="_ _c"> </span>coinciden<span class="_ _f"> </span>tam<span class="_ _3"></span>bi´<span class="_ _a"></span>en</div><div class="t m0 xa h7 y115 ff6 fs3 fc0 sc0 ls0 ws0">Esto<span class="_ _c"> </span>genera<span class="_ _c"> </span>resultados<span class="_ _c"> </span>a<span class="_ _c"> </span>destacar,<span class="_ _c"> </span>veamos...</div><div class="t m0 x34 h7 y116 ff6 fs3 fc0 sc0 ls0 ws0">Sean<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">→<span class="_ _20"> </span></span></span>longitud<span class="_ _e"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>lados</div><div class="t m0 x13 h7 y117 ff8 fs3 fc0 sc0 ls0 ws0">h<span class="_ _20"> </span><span class="ffa">→<span class="_ _20"> </span><span class="ff6">altura<span class="_ _e"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>lados</span></span></div><div class="t m0 x8d h7 y118 ff8 fs3 fc0 sc0 ls0 ws0">S<span class="_ _c"> </span><span class="ffa">→<span class="_ _20"> </span><span class="ff6">´<span class="_ _d"></span>area<span class="_ _c"> </span>del<span class="_ _f"> </span>tri´<span class="_ _d"></span>angulo</span></span></div><div class="t m0 x8e h7 y119 ff8 fs3 fc0 sc0 ls0 ws0">r<span class="_ _e"> </span><span class="ffa">→<span class="_ _20"> </span><span class="ff6">radio<span class="_ _e"> </span>de<span class="_ _f"> </span>la<span class="_ _e"> </span>circunferencia<span class="_ _c"> </span>inscrita</span></span></div><div class="t m0 x36 h7 y11a ff8 fs3 fc0 sc0 ls0 ws0">R<span class="_ _20"> </span><span class="ffa">→<span class="_ _20"> </span><span class="ff6">radio<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>circunferencia<span class="_ _c"> </span>circunscrita</span></span></div><div class="t m0 x8f h7 y11b ffa fs3 fc0 sc0 ls0 ws0">∗<span class="_ _20"> </span><span class="ff6">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _31"> </span><span class="ff8">h<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>R<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>r<span class="_ _32"> </span>R<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>2</span>r<span class="_ _32"> </span>h<span class="_ _20"> </span><span class="ff6">=</span></span></span></span></div><div class="t m0 x90 h7 y11c ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x24 h7 y11d ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 x25 h7 y11e ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x91 h7 y11b ff8 fs3 fc0 sc0 ls0 ws0">a<span class="_ _31"> </span>S<span class="_ _c"> </span><span class="ff6">=</span></div><div class="t m0 x92 h9 y11d ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x93 ha y11f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x94 h7 y11c ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 xc h7 y11d ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 x95 h7 y11e ff6 fs3 fc0 sc0 ls0 ws0">4</div><div class="t m0 xa h7 y120 ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _20"> </span>que<span class="_ _e"> </span>es<span class="_ _e"> </span>suficiente<span class="_"> </span>cono<span class="_ _24"></span>cer<span class="_ _e"> </span>cualesquiera<span class="_ _e"> </span>dos<span class="_ _20"> </span>de<span class="_ _e"> </span>estas<span class="_ _e"> </span>v<span class="_ _3"></span>ariables<span class="_ _e"> </span>para<span class="_ _20"> </span>p<span class="_ _24"></span>o<span class="_ _24"></span>der<span class="_ _e"> </span>cono<span class="_ _24"></span>cer<span class="_ _e"> </span>el</div><div class="t m0 xb h7 y121 ff6 fs3 fc0 sc0 ls0 ws0">v<span class="_ _3"></span>alor<span class="_ _e"> </span>de<span class="_ _f"> </span>las<span class="_ _e"> </span>otras<span class="_ _c"> </span>3.</div><div class="t m0 xb h7 y122 ff6 fs3 fc0 sc0 ls0 ws0">Otras<span class="_ _c"> </span>notas<span class="_ _c"> </span>de<span class="_ _c"> </span>inter<span class="_ _3"></span>´<span class="_ _a"></span>es</div><div class="t m0 x5e h7 y123 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Sean<span class="_ _13"> </span><span class="ff8">b</span></div><div class="t m0 x8f he y124 ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x4d h7 y123 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _13"> </span><span class="ff8">b</span></div><div class="t m0 x43 he y125 ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 x88 h7 y123 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _13"> </span><span class="ff8">b</span></div><div class="t m0 x96 he y124 ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 x46 h7 y123 ffa fs3 fc0 sc0 ls0 ws0">→<span class="_ _13"> </span><span class="ff6">longitud<span class="_ _13"> </span>de<span class="_ _8"> </span>las<span class="_ _13"> </span>bisectrices<span class="_ _8"> </span>de<span class="_ _13"> </span><span class="ff8">a</span>,<span class="_ _13"> </span><span class="ff8">b<span class="_ _8"> </span></span>y<span class="_ _13"> </span><span class="ff8">c<span class="_ _8"> </span></span>y<span class="_ _13"> </span><span class="ff8">p<span class="_ _13"> </span></span></span>→<span class="_ _8"> </span><span class="ff6">semip<span class="_ _24"></span>er<span class="_ _10"></span>´<span class="_ _11"></span>ımetro<span class="_ _13"> </span>del</span></div><div class="t m0 x5f h7 y126 ff6 fs3 fc0 sc0 ls0 ws0">tri´<span class="_ _d"></span>angulo</div><div class="t m0 x5f h7 y127 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">b</span></span></div><div class="t m0 x31 he y128 ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x97 h7 y127 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x2d h7 y129 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2c h7 y12a ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c</div><div class="t m0 x3a hb y12b ffb fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x67 h7 y127 ff8 fs3 fc0 sc0 ls0 ws0">bc<span class="ff6">(</span>p<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a<span class="ff6">)<span class="_ _c"> </span>y<span class="_ _c"> </span>as<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>con<span class="_ _c"> </span><span class="ff8">b</span></span></div><div class="t m0 x98 he y12c ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 x71 h7 y127 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">b</span></div><div class="t m0 x99 he y128 ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 x5e h7 y49 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Sean<span class="_ _e"> </span><span class="ff8">m</span></div><div class="t m0 x81 he y12d ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x9a h7 y49 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">m</span></div><div class="t m0 x12 he y12e ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 x96 h9 y49 ff8 fs3 fc0 sc0 ls0 ws0">m</div><div class="t m0 x2e he y12d ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 x2f h7 y49 ffa fs3 fc0 sc0 ls0 ws0">→<span class="_ _c"> </span><span class="ff6">longitud<span class="_ _c"> </span>de<span class="_ _c"> </span>las<span class="_ _c"> </span>medianas<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="_ _f"> </span><span class="ff8">a</span>,<span class="_ _e"> </span><span class="ff8">b<span class="_ _c"> </span></span>y<span class="_ _f"> </span><span class="ff8">c</span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">6</div><div class="t m0 x5f h7 y12f ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">m</span></span></div><div class="t m0 x2b he y130 ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x9b h7 y12f ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x9c h7 y131 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x9c h7 y132 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12 hb y133 ffb fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x5b h7 y134 ff6 fs3 fc0 sc0 ls0 ws0">2(<span class="ff8">b</span></div><div class="t m0 x2f ha y135 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9d h7 y134 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 x10 ha y135 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9e h7 y134 ff6 fs3 fc0 sc0 ls0 ws0">)<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span><span class="ff8">a</span></span></div><div class="t m0 x9f ha y135 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa0 h7 y134 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span>as<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>con<span class="_ _c"> </span><span class="ff8">m</span></div><div class="t m0 xa1 he y136 ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 xa2 h7 y12f ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">m</span></div><div class="t m0 x57 he y130 ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 x5e h7 y137 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Sean<span class="_ _e"> </span><span class="ff8">h</span></div><div class="t m0 xa3 he y138 ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 xa4 h7 y137 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">h</span></div><div class="t m0 xa5 he y139 ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 x2d h7 y137 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">h</span></div><div class="t m0 xa6 he y138 ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 xa7 h7 y137 ffa fs3 fc0 sc0 ls0 ws0">→<span class="_ _c"> </span><span class="ff6">longitud<span class="_ _c"> </span>de<span class="_ _c"> </span>las<span class="_ _c"> </span>alturas<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="ff8">a</span>,<span class="_ _f"> </span><span class="ff8">b<span class="_ _e"> </span></span>y<span class="_ _c"> </span><span class="ff8">c</span></span></div><div class="t m0 x5f h7 y13a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">h</span></span></div><div class="t m0 x42 he y13b ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x81 h7 y13a ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x43 h7 y13c ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa8 h9 y13d ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x2d hb y13e ffb fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x96 h7 y13a ff8 fs3 fc0 sc0 ls0 ws0">ρ<span class="ff6">(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>b<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>c<span class="ff6">)<span class="_ _c"> </span>y<span class="_ _c"> </span>as<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>con<span class="_ _c"> </span><span class="ff8">h</span></span></div><div class="t m0 x57 he y13f ffd fs4 fc0 sc0 ls0 ws0">b</div><div class="t m0 xa9 h7 y13a ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">h</span></div><div class="t m0 xaa he y13b ffd fs4 fc0 sc0 ls0 ws0">c</div><div class="t m0 x5e h7 y140 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Sean<span class="_ _e"> </span><span class="ff8">K<span class="_ _13"> </span></span>circuncentro,<span class="_ _e"> </span><span class="ff8">I<span class="_ _8"> </span></span>incen<span class="_ _12"></span>tro,<span class="_ _c"> </span><span class="ff8">R<span class="_ _c"> </span></span>circunradio<span class="_ _c"> </span>y<span class="_ _c"> </span><span class="ff8">r<span class="_ _f"> </span></span>inradio</div><div class="t m0 x5f h7 y141 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff6">(<span class="ff8">K<span class="_ _28"></span>I<span class="_ _28"></span></span>)</span></span></div><div class="t m0 x2 ha y142 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x88 h7 y141 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">R</span></div><div class="t m0 xab ha y142 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xac h7 y141 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff6">2<span class="ff8">Rr<span class="_ _f"> </span></span>(f´<span class="_ _d"></span>ormula<span class="_ _e"> </span>de<span class="_ _c"> </span>Euler)</span></div><div class="t m0 x5e h7 y143 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Simedianas<span class="_ _8"> </span>de<span class="_ _6"> </span>un<span class="_ _8"> </span>tri´<span class="_ _d"></span>angulo:<span class="_ _6"> </span>En<span class="_ _8"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _28"></span></span></span>:<span class="_ _8"> </span><span class="ff8">AM<span class="_ _30"> </span></span>mediana,<span class="_ _6"> </span><span class="ff8">AD<span class="_ _6"> </span></span>bisectriz<span class="_ _8"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _6"> </span><span class="ff8">AX<span class="_ _16"> </span><span class="ff6">es</span></span></span></div><div class="t m0 x5f h7 y144 ff6 fs3 fc0 sc0 ls0 ws0">simediana<span class="_ _c"> </span>de<span class="_ _c"> </span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _13"> </span></span>si<span class="_ _c"> </span><span class="ff8">AD<span class="_ _f"> </span></span>biseca<span class="_ _c"> </span>al<span class="_ _c"> </span><span class="ffc">]<span class="ff8">X<span class="_ _28"></span>AM<span class="_ _6"> </span></span></span>y<span class="_ _e"> </span>se<span class="_ _c"> </span>cumple:</div><div class="t m0 x76 h9 y145 ff8 fs3 fc0 sc0 ls0 ws0">X<span class="_ _28"></span>B</div><div class="t m0 x76 h9 y146 ff8 fs3 fc0 sc0 ls0 ws0">X<span class="_ _28"></span>C</div><div class="t m0 x31 h7 y147 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x4d h9 y145 ff8 fs3 fc0 sc0 ls0 ws0">AB</div><div class="t m0 x32 ha y148 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa4 h9 y149 ff8 fs3 fc0 sc0 ls0 ws0">AC</div><div class="t m0 x32 ha y14a ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x79 h7 y147 ff6 fs3 fc0 sc0 ls0 ws0">El<span class="_ _21"> </span>pun<span class="_ _3"></span>to<span class="_"> </span>donde<span class="_ _1e"> </span>las<span class="_"> </span>tres<span class="_ _1e"> </span>simedianas<span class="_ _21"> </span>se<span class="_ _21"> </span>cortan<span class="_ _1e"> </span>s<span class="_ _24"></span>e<span class="_ _1e"> </span>llama<span class="_"> </span>Pun<span class="_ _3"></span>to<span class="_ _21"> </span>de<span class="_ _21"> </span>Lemoine</div><div class="t m0 x5e h7 y14b ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _c"> </span>-<span class="_ _16"> </span>Los<span class="_ _c"> </span>segmentos<span class="_ _e"> </span>trazados<span class="_ _f"> </span>desde<span class="_ _c"> </span>cada<span class="_ _f"> </span>v<span class="_ _3"></span>´<span class="_ _25"></span>ertice<span class="_ _c"> </span>de<span class="_ _f"> </span>un<span class="_ _c"> </span>tri´<span class="_ _a"></span>angulo<span class="_ _c"> </span>dado<span class="_ _c"> </span>con<span class="_ _f"> </span>el<span class="_ _c"> </span>v´<span class="_ _a"></span>ertice<span class="_ _c"> </span>m´<span class="_ _a"></span>as</div><div class="t m0 x5f h7 y14c ff6 fs3 fc0 sc0 ls0 ws0">alejado<span class="_"> </span>del<span class="_"> </span>tri´<span class="_ _d"></span>angulo<span class="_"> </span>equil´<span class="_ _d"></span>atero<span class="_"> </span>trazado<span class="_"> </span>exteriormen<span class="_ _3"></span>te<span class="_"> </span>a<span class="_"> </span>dic<span class="_ _12"></span>ho<span class="_"> </span>tri´<span class="_ _d"></span>angulo<span class="_"> </span>sobre<span class="_"> </span>el<span class="_"> </span>lado</div><div class="t m0 x5f h7 y14d ff6 fs3 fc0 sc0 ls0 ws0">opuesto<span class="_ _f"> </span>al<span class="_ _13"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _13"> </span>dado<span class="_ _f"> </span>son<span class="_ _13"> </span>iguales.<span class="_ _f"> </span>Estos<span class="_ _f"> </span>tres<span class="_ _13"> </span>segmen<span class="_ _3"></span>tos<span class="_ _13"> </span>se<span class="_ _f"> </span>cortan<span class="_ _13"> </span>en<span class="_ _f"> </span>un<span class="_ _13"> </span>pun<span class="_ _3"></span>to</div><div class="t m0 x5f h7 y14e ff6 fs3 fc0 sc0 ls0 ws0">llamado:<span class="_ _c"> </span>Pun<span class="_ _12"></span>to<span class="_ _c"> </span>de<span class="_ _c"> </span>F<span class="_ _b"></span>ermat</div><div class="t m0 xb h7 y14f ff6 fs3 fc0 sc0 ls0 ws0">4,<span class="_ _c"> </span>5,<span class="_ _c"> </span>6,<span class="_ _c"> </span>...<span class="_ _c"> </span>pueden<span class="_ _c"> </span>ser<span class="_ _c"> </span>sugerencias<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>amigos<span class="_ _c"> </span>de<span class="_ _f"> </span>la<span class="_ _e"> </span>matem´<span class="_ _a"></span>atica<span class="_ _e"> </span>a<span class="_ _f"> </span>estos<span class="_ _e"> </span>temas</div><div class="t m0 x69 h7 y150 ff5 fs3 fc0 sc0 ls0 ws0">Las<span class="_ _f"> </span>notas<span class="_ _13"> </span>marcadas<span class="_ _f"> </span>con<span class="_ _13"> </span>*<span class="_ _f"> </span>deb<span class="_ _24"></span>en<span class="_ _13"> </span>ser<span class="_ _f"> </span>demostradas</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">7</div><div class="t m0 xb h5 yc1 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#3<span class="_ _6"> </span>-<span class="_ _16"> </span>Circunferencia<span class="_ _6"> </span>y<span class="_ _16"> </span>Cuadril´<span class="_ _7"></span>atero</div><div class="t m0 xa h7 yc2 ff6 fs3 fc0 sc0 ls0 ws0">An<span class="_ _3"></span>tes<span class="_ _e"> </span>de<span class="_ _e"> </span>proseguir<span class="_"> </span>quiero<span class="_ _e"> </span>se<span class="_ _24"></span>˜<span class="_ _d"></span>nalar<span class="_"> </span>que<span class="_ _e"> </span>esto<span class="_"> </span>no<span class="_ _e"> </span>es<span class="_ _e"> </span>un<span class="_"> </span>comp<span class="_ _24"></span>endio<span class="_ _e"> </span>sobre<span class="_ _e"> </span>temas<span class="_"> </span>de<span class="_ _e"> </span>nuestra</div><div class="t m0 xb h7 yc3 ff6 fs3 fc0 sc0 ls0 ws0">ense<span class="_ _24"></span>˜<span class="_ _d"></span>nanza,<span class="_ _e"> </span>mi<span class="_ _e"> </span>may<span class="_ _3"></span>or<span class="_ _e"> </span>anhelo<span class="_ _c"> </span>es<span class="_ _e"> </span>colab<span class="_ _24"></span>orar<span class="_ _c"> </span>con<span class="_ _e"> </span>la<span class="_ _c"> </span>cultura<span class="_ _e"> </span>matem´<span class="_ _a"></span>atica<span class="_ _e"> </span>sobre<span class="_ _e"> </span>to<span class="_ _24"></span>do<span class="_ _c"> </span>con<span class="_ _c"> </span>notas</div><div class="t m0 xb h7 yc4 ff6 fs3 fc0 sc0 ls0 ws0">p<span class="_ _24"></span>o<span class="_ _24"></span>co<span class="_ _c"> </span>publicadas<span class="_ _c"> </span>y<span class="_ _c"> </span>que<span class="_ _c"> </span>sean<span class="_ _c"> </span>muy<span class="_ _e"> </span>interesan<span class="_ _3"></span>tes...</div><div class="t m0 xb h7 y151 ff6 fs3 fc0 sc0 ls0 ws0">1)<span class="_ _1e"> </span>Y<span class="_ _b"></span>a<span class="_ _1e"> </span>vimos<span class="_ _1e"> </span>que<span class="_ _1e"> </span>en<span class="_ _1e"> </span>to<span class="_ _24"></span>do<span class="_ _1e"> </span>tri´<span class="_ _d"></span>angulo<span class="_ _1e"> </span>puede<span class="_ _1e"> </span>inscribirse<span class="_ _1e"> </span>y<span class="_ _21"> </span>circunscribirse<span class="_ _1e"> </span>una<span class="_ _1e"> </span>circunferencia.<span class="_ _1e"> </span>Sin</div><div class="t m0 xb h7 y152 ff6 fs3 fc0 sc0 ls0 ws0">em<span class="_ _3"></span>bargo<span class="_ _c"> </span>este<span class="_ _c"> </span>privilegio<span class="_ _c"> </span>no<span class="_ _c"> </span>lo<span class="_ _c"> </span>p<span class="_ _24"></span>oseen<span class="_ _c"> </span>los<span class="_ _e"> </span>cuadril´<span class="_ _a"></span>ateros.<span class="_ _e"> </span>Para<span class="_ _e"> </span>que<span class="_ _c"> </span>una<span class="_ _c"> </span>circunferencia<span class="_ _c"> </span>pueda</div><div class="t m0 xb h7 yc7 ff6 fs3 fc0 sc0 ls0 ws0">circunscribirse<span class="_ _8"> </span>en<span class="_ _13"> </span>un<span class="_ _8"> </span>cuadril´<span class="_ _a"></span>atero<span class="_ _13"> </span><span class="ff8">AB<span class="_ _9"></span>C<span class="_ _28"></span>D<span class="_ _6"> </span></span>tiene<span class="_ _13"> </span>que<span class="_ _8"> </span>cumplirse<span class="_ _8"> </span>que<span class="_ _8"> </span>los<span class="_ _13"> </span>´<span class="_ _a"></span>angulos<span class="_ _13"> </span>opuestos</div><div class="t m0 xb h7 y153 ff6 fs3 fc0 sc0 ls0 ws0">sean<span class="_ _f"> </span>suplementarios<span class="_ _f"> </span>(<span class="ffc">]<span class="ff8">A<span class="_ _1e"> </span></span></span>+<span class="_"> </span><span class="ffc">]<span class="ff8">C<span class="_ _13"> </span></span></span>=<span class="_ _f"> </span>180</div><div class="t m0 xad h8 y154 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x9 h7 y153 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _f"> </span><span class="ffc">]<span class="ff8">B<span class="_ _e"> </span></span></span>+<span class="_ _21"> </span><span class="ffc">]<span class="ff8">D<span class="_ _f"> </span></span></span>=<span class="_ _f"> </span>180</div><div class="t m0 xaa h8 y154 ff7 fs4 fc0 sc0 ls0 ws0">◦</div><div class="t m0 x6e h7 y153 ff6 fs3 fc0 sc0 ls0 ws0">),<span class="_ _f"> </span>este<span class="_ _f"> </span>cuadril´<span class="_ _a"></span>atero<span class="_ _f"> </span>es<span class="_ _f"> </span>llamado</div><div class="t m0 xb h7 y155 ff6 fs3 fc0 sc0 ls0 ws0">Cuadril´<span class="_ _d"></span>atero<span class="_ _c"> </span>C<span class="_ _10"></span>´<span class="_ _11"></span>ıclico<span class="_ _c"> </span>(<span class="ff8">C<span class="_ _28"></span>C<span class="_ _28"></span></span>).</div><div class="t m0 x69 h7 y156 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_"> </span>para<span class="_"> </span>que<span class="_"> </span>pueda<span class="_ _21"> </span>ser<span class="_"> </span>inscrito<span class="_"> </span>tiene<span class="_"> </span>que<span class="_ _21"> </span>cumplir<span class="_"> </span>que<span class="_"> </span><span class="ff8">AB<span class="_ _29"> </span></span>+<span class="_ _27"></span><span class="ff8">C<span class="_ _9"></span>D<span class="_ _e"> </span></span>=<span class="_"> </span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _1f"> </span></span>+<span class="_ _27"></span><span class="ff8">D<span class="_ _24"></span>A</span></div><div class="t m0 xb h7 y157 ff6 fs3 fc0 sc0 ls0 ws0">(T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Pitot).</div><div class="t m0 xa h7 y158 ff6 fs3 fc0 sc0 ls0 ws0">Cono<span class="_ _24"></span>cer<span class="_ _c"> </span>esto<span class="_ _c"> </span>es<span class="_ _c"> </span>muy<span class="_ _e"> </span>ven<span class="_ _3"></span>ta<span class="_ _9"></span>joso,<span class="_ _c"> </span>pues<span class="_ _c"> </span>veamos...</div><div class="t m0 x30 h9 y159 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 y15a ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xae h9 y15b ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x7b h9 y15c ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 xae h9 y15d ff8 fs3 fc0 sc0 ls0 ws0">E</div><div class="t m0 xaf h9 y15e ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xb0 h9 y15f ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x3 h9 y160 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xb1 h7 y161 ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 x47 h7 y162 ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xb2 h7 y163 ff6 fs3 fc0 sc0 ls0 ws0">Sea<span class="_"> </span><span class="ff8">AB<span class="_ _24"></span>C<span class="_ _28"></span>D<span class="_ _20"> </span></span>un<span class="_"> </span><span class="ff8">C<span class="_ _9"></span>C<span class="_ _f"> </span></span>tal<span class="_ _21"> </span>que<span class="_"> </span>sus<span class="_ _21"> </span>diagonales<span class="_"> </span>se<span class="_"> </span>cortan<span class="_ _1e"> </span>en<span class="_"> </span><span class="ff8">P<span class="_ _13"> </span></span>=<span class="_ _4"></span><span class="ffa">⇒</span></div><div class="t m0 xb3 h7 y164 ff6 fs3 fc0 sc0 ls0 ws0">i<span class="_ _c"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _16"> </span><span class="ffc">]<span class="ff8">AB<span class="_ _24"></span>D<span class="_ _e"> </span></span></span>=<span class="_"> </span><span class="ffc">]<span class="ff8">AC<span class="_ _28"></span>D<span class="_ _24"></span></span></span>,<span class="_ _c"> </span><span class="ffc">]<span class="ff8">D<span class="_ _24"></span>B<span class="_ _9"></span>C<span class="_ _f"> </span></span></span>=<span class="_"> </span><span class="ffc">]<span class="ff8">D<span class="_ _24"></span>AC<span class="_ _9"></span></span></span>,<span class="_ _c"> </span>etc</div><div class="t m0 xb4 h7 y165 ff6 fs3 fc0 sc0 ls0 ws0">ii<span class="_ _c"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _16"> </span><span class="ffc">]<span class="ff8">DAB<span class="_ _c"> </span></span></span>=<span class="_"> </span><span class="ffc">]<span class="ff8">D<span class="_ _24"></span>C<span class="_ _28"></span>E<span class="_ _13"> </span></span></span>(siendo<span class="_ _c"> </span><span class="ff8">B<span class="_ _9"></span></span>,<span class="_ _c"> </span><span class="ff8">C<span class="_ _13"> </span></span>y<span class="_ _c"> </span><span class="ff8">E<span class="_ _13"> </span></span>alineados)</div><div class="t m0 xb5 h7 y166 ff6 fs3 fc0 sc0 ls0 ws0">iii<span class="_ _c"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _16"> </span><span class="ff8">AP<span class="_ _c"> </span><span class="ffa">·<span class="_ _1e"> </span></span>P<span class="_ _1f"> </span>C<span class="_ _c"> </span></span>=<span class="_"> </span><span class="ff8">D<span class="_ _24"></span>P<span class="_ _f"> </span><span class="ffa">·<span class="_ _1e"> </span></span>P<span class="_ _29"> </span>B<span class="_ _13"> </span></span>(p<span class="_ _24"></span>otencia<span class="_ _c"> </span>de<span class="_ _c"> </span>un<span class="_ _c"> </span>punto<span class="_ _e"> </span>PP)</div><div class="t m0 xb5 h7 y167 ff6 fs3 fc0 sc0 ls0 ws0">iv<span class="_ _c"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _16"> </span><span class="ff8">AB<span class="_ _27"> </span><span class="ffa">·<span class="_ _28"></span></span>C<span class="_ _28"></span>D<span class="_ _27"></span></span>+<span class="_ _28"></span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _1f"> </span><span class="ffa">·<span class="_ _9"></span></span>D<span class="_ _9"></span>A<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">AC<span class="_ _29"> </span><span class="ffa">·<span class="_ _28"></span></span>B<span class="_ _9"></span>D<span class="_ _e"> </span></span>(T<span class="_ _b"></span>eorema<span class="_"> </span>de<span class="_ _21"> </span>Ptolomeo)</div><div class="t m0 xb4 h7 y168 ff6 fs3 fc0 sc0 ls0 ws0">v<span class="_ _c"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _16"> </span><span class="ff8">A</span></div><div class="t m0 x53 he y169 ffd fs4 fc0 sc0 ls0 ws0">AB<span class="_ _24"></span>C<span class="_ _9"></span>D</div><div class="t m0 xb6 h7 y168 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xb7 hb y16a ffb fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 xb8 h7 y168 ff8 fs3 fc0 sc0 ls0 ws0">ρ<span class="ff6">(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>b<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>c<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>d<span class="ff6">)</span></div><div class="t m0 x83 h7 y16b ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">ρ<span class="_ _c"> </span></span>semip<span class="_ _24"></span>er<span class="_ _10"></span>´<span class="_ _11"></span>ımetro)</div><div class="t m0 xb h7 y16c ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_"> </span>m<span class="_ _3"></span>uc<span class="_ _12"></span>has<span class="_"> </span>otras<span class="_ _1e"> </span>relaciones,<span class="_"> </span>y<span class="_"> </span>como<span class="_ _1e"> </span>sab<span class="_ _24"></span>emos,<span class="_"> </span>la<span class="_"> </span>Geometr<span class="_ _4"></span>´<span class="_ _11"></span>ıa<span class="_"> </span>es<span class="_"> </span>el<span class="_ _21"> </span>arte<span class="_"> </span>de<span class="_ _1e"> </span>relacionar<span class="_"> </span>elemen<span class="_ _3"></span>tos</div><div class="t m0 xb h7 y16d ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>las<span class="_ _c"> </span>figuras<span class="_ _c"> </span>presentadas.</div><div class="t m0 xb h7 y16e ff6 fs3 fc0 sc0 ls0 ws0">2)<span class="_ _f"> </span>Potencia<span class="_ _f"> </span>de<span class="_ _f"> </span>un<span class="_ _f"> </span>punto:<span class="_ _f"> </span>Puede<span class="_ _f"> </span>presentarse<span class="_ _f"> </span>de<span class="_ _f"> </span>v<span class="_ _3"></span>arias<span class="_ _f"> </span>formas,<span class="_ _f"> </span>ver<span class="_ _f"> </span>que<span class="_ _f"> </span>en<span class="_ _13"> </span>1.iii<span class="_ _f"> </span><span class="ffa">4<span class="ff8">AP<span class="_ _29"> </span>B<span class="_ _13"> </span></span>∼</span></div><div class="t m0 xb h7 y16f ffa fs3 fc0 sc0 ls0 ws0">4<span class="ff8">C<span class="_ _9"></span>P<span class="_ _1f"> </span>D<span class="ff6">,<span class="_ _f"> </span>esta<span class="_ _e"> </span>ser<span class="_ _10"></span>´<span class="_ _11"></span>ıa<span class="_ _c"> </span>la<span class="_ _c"> </span>primera<span class="_ _c"> </span>forma.</span></span></div><div class="t m0 xa h7 y170 ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>2)</div><div class="t m0 x7b h9 y171 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xae h9 y172 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xb9 h9 y173 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x67 h9 y174 ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x15 h7 y175 ff6 fs3 fc0 sc0 ls0 ws0">Si<span class="_ _c"> </span><span class="ff8">C<span class="_ _28"></span>D<span class="_ _f"> </span></span>tangen<span class="_ _3"></span>te<span class="_ _c"> </span>en<span class="_ _c"> </span><span class="ff8">D</span></div><div class="t m0 x15 h7 y176 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">D<span class="_ _24"></span>C</span></span></div><div class="t m0 xba ha y177 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xbb h7 y176 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">AC<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"> </span></span>B<span class="_ _9"></span>C</span></div><div class="t m0 x15 h7 y178 ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _c"> </span>que<span class="_ _c"> </span><span class="ffa">4<span class="ff8">AC<span class="_ _28"></span>D<span class="_ _e"> </span></span>∼<span class="_ _20"> </span>4<span class="ff8">D<span class="_ _24"></span>B<span class="_ _24"></span>C</span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">8</div><div class="t m0 xa h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>3)</div><div class="t m0 x7b h9 y179 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x21 h9 y17a ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xbc h9 y17b ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 xbd h9 y17c ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x4 h9 y17d ff8 fs3 fc0 sc0 ls0 ws0">E</div><div class="t m0 x15 h7 y17e ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _9"></span>E<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"> </span></span>D<span class="_ _24"></span>C<span class="_ _f"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _28"></span>A<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>B<span class="_ _24"></span>C</div><div class="t m0 x15 h7 y17f ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _c"> </span>que<span class="_ _c"> </span><span class="ffa">4<span class="ff8">AC<span class="_ _28"></span>D<span class="_ _e"> </span></span>∼<span class="_ _20"> </span>4<span class="ff8">B<span class="_ _24"></span>C<span class="_ _28"></span>E</span></span></div><div class="t m0 xb h7 y180 ff6 fs3 fc0 sc0 ls0 ws0">3)<span class="_ _c"> </span>Eje<span class="_ _c"> </span>radical<span class="_ _c"> </span>de<span class="_ _c"> </span>dos<span class="_ _c"> </span>circunferencias<span class="_ _c"> </span>(<span class="ff8">E<span class="_ _28"></span>R</span>)</div><div class="t m0 xa h7 y181 ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>eamos<span class="_ _c"> </span>las<span class="_ _c"> </span>formas<span class="_ _c"> </span>de<span class="_ _c"> </span>presentarse</div><div class="t m0 xb h7 y182 ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>1</div><div class="t m0 x5a h7 y183 ff6 fs3 fc0 sc0 ls0 ws0">Circunferencias<span class="_ _c"> </span>T<span class="_ _b"></span>angen<span class="_ _12"></span>tes</div><div class="t m0 xa8 h7 y184 ff6 fs3 fc0 sc0 ls0 ws0">Externas</div><div class="t m0 x87 h9 y185 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 x5f ha y186 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x67 h9 y185 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 x9d ha y186 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb0 h9 y187 ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xbe h7 y188 ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>2</div><div class="t m0 x17 h7 y189 ff6 fs3 fc0 sc0 ls0 ws0">Circunferencias</div><div class="t m0 xbf h7 y18a ff6 fs3 fc0 sc0 ls0 ws0">Exteriores</div><div class="t m0 xc0 h9 y18b ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xc1 ha y18c ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xc2 h9 y18b ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xc3 ha y18c ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xc4 h9 y18d ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xb h7 y18e ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>3</div><div class="t m0 x5a h7 y18f ff6 fs3 fc0 sc0 ls0 ws0">Circunferencias<span class="_ _c"> </span>T<span class="_ _b"></span>angen<span class="_ _12"></span>tes</div><div class="t m0 xc5 h7 y190 ff6 fs3 fc0 sc0 ls0 ws0">In<span class="_ _3"></span>teriores</div><div class="t m0 x40 h9 y191 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xc6 ha y192 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa4 h9 y191 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xc5 ha y192 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7b h9 y193 ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xbe h7 y194 ff6 fs3 fc0 sc0 ls0 ws0">forma<span class="_ _c"> </span>4</div><div class="t m0 x17 h7 y195 ff6 fs3 fc0 sc0 ls0 ws0">Circunferencias</div><div class="t m0 xc7 h7 y196 ff6 fs3 fc0 sc0 ls0 ws0">Secan<span class="_ _3"></span>tes</div><div class="t m0 xc8 h9 y197 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xaa ha y198 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x27 h9 y197 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xc9 ha y198 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xca h9 y199 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xca h9 y19a ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x1e h9 y19b ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xca h9 y19c ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xcb h9 y19d ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x27 h9 y19e ff8 fs3 fc0 sc0 ls0 ws0">T</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">9</div><div class="t m0 xa h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">En<span class="_ _13"> </span>cada<span class="_ _8"> </span>forma<span class="_ _8"> </span>vemos<span class="_ _13"> </span>que<span class="_ _8"> </span><span class="ff8">E<span class="_ _9"></span>R<span class="_ _8"> </span><span class="ffa">⊥<span class="_ _8"> </span></span>O</span></div><div class="t m0 xcc ha y19f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x7 h9 y9 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 x98 ha y19f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xcd h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _13"> </span>p<span class="_ _24"></span>ero<span class="_ _8"> </span>lo<span class="_ _8"> </span>m´<span class="_ _a"></span>as<span class="_ _13"> </span>destacado<span class="_ _8"> </span>es<span class="_ _8"> </span>que:<span class="_ _13"> </span>T<span class="_ _b"></span>o<span class="_ _24"></span>do<span class="_ _8"> </span>punto</div><div class="t m0 xb h7 y81 ff6 fs3 fc0 sc0 ls0 ws0">situado<span class="_ _8"> </span>en<span class="_ _8"> </span>el<span class="_ _8"> </span><span class="ff8">E<span class="_ _28"></span>R<span class="_ _8"> </span></span>tiene<span class="_ _8"> </span>la<span class="_ _6"> </span>misma<span class="_ _13"> </span>p<span class="_ _24"></span>otencia<span class="_ _8"> </span>resp<span class="_ _24"></span>ecto<span class="_ _6"> </span>a<span class="_ _13"> </span>ambas<span class="_ _13"> </span>circunferencias.<span class="_ _6"> </span>V<span class="_ _10"></span>ea<span class="_ _8"> </span>como</div><div class="t m0 xb h7 y1a0 ff6 fs3 fc0 sc0 ls0 ws0">ejemplo<span class="_ _c"> </span>en<span class="_ _c"> </span>la<span class="_ _c"> </span>forma<span class="_ _c"> </span>4<span class="_ _c"> </span><span class="ff8">P<span class="_ _1f"> </span>Q</span></div><div class="t m0 x13 ha y1a1 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x68 h7 y1a0 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">P<span class="_ _29"> </span>B<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"> </span></span>P<span class="_ _29"> </span>A<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">P<span class="_ _29"> </span>T</span></div><div class="t m0 x55 ha y1a1 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x72 h7 y1a0 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span>siendo<span class="_ _c"> </span><span class="ff8">P<span class="_ _29"> </span>Q<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">P<span class="_ _1f"> </span>T<span class="_ _6"> </span></span>tangen<span class="_ _3"></span>tes.</div><div class="t m0 xb h7 y1a2 ff6 fs3 fc0 sc0 ls0 ws0">4)<span class="_ _c"> </span>Cen<span class="_ _12"></span>tro<span class="_ _c"> </span>radical<span class="_ _c"> </span>de<span class="_ _c"> </span>3<span class="_ _c"> </span>circunferencias<span class="_ _c"> </span>(<span class="ff8">C<span class="_ _28"></span>R</span>).</div><div class="t m0 x5f h9 y1a3 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xce ha y1a4 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x5 h9 y1a5 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xcf ha y1a6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3c h9 y1a7 ff8 fs3 fc0 sc0 ls0 ws0">O</div><div class="t m0 xd0 ha y1a8 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x6b h9 y1a9 ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _9"></span>R</div><div class="t m0 xd1 h9 y1aa ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 x4e h9 y1ab ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xd2 h9 y1ac ff8 fs3 fc0 sc0 ls0 ws0">E<span class="_ _9"></span>R</div><div class="t m0 xd3 h7 y1ad ff6 fs3 fc0 sc0 ls0 ws0">Es<span class="_ _c"> </span>el<span class="_ _c"> </span>punto</div><div class="t m0 xd4 h7 y1ae ff6 fs3 fc0 sc0 ls0 ws0">donde<span class="_ _c"> </span>concurren</div><div class="t m0 xd3 h7 y1af ff6 fs3 fc0 sc0 ls0 ws0">los<span class="_ _c"> </span>tres<span class="_ _c"> </span><span class="ff8">E<span class="_ _9"></span>R</span></div><div class="t m0 xb h7 y1b0 ff6 fs3 fc0 sc0 ls0 ws0">5)<span class="_ _c"> </span>T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Ptolomeo</div><div class="t m0 xa h7 y1b1 ff6 fs3 fc0 sc0 ls0 ws0">Como<span class="_ _c"> </span>vimos<span class="_ _f"> </span>en<span class="_ _c"> </span>1.iv,<span class="_ _c"> </span>en<span class="_ _f"> </span>todo<span class="_ _f"> </span><span class="ff8">C<span class="_ _9"></span>C<span class="_ _8"> </span></span>el<span class="_ _c"> </span>pro<span class="_ _24"></span>ducto<span class="_ _f"> </span>de<span class="_ _c"> </span>las<span class="_ _c"> </span>diagonales<span class="_ _f"> </span>es<span class="_ _c"> </span>igual<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _c"> </span>suma<span class="_ _c"> </span>del</div><div class="t m0 xb h7 y1b2 ff6 fs3 fc0 sc0 ls0 ws0">pro<span class="_ _24"></span>ducto<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="_ _c"> </span>opuestos.</div><div class="t m0 x7d h9 y1b3 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xd5 h9 y1b4 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x68 h9 y1b5 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x7b h9 y1b6 ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 xa8 h9 y1b7 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x96 h9 y1b8 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x2a h9 y1b9 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x6b h9 y1ba ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x9b h7 y1bb ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xd6 h7 y1bc ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xb2 h7 y1bd ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>B<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"></span></span>C<span class="_ _9"></span>A<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>AB<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"> </span></span>C<span class="_ _9"></span>D<span class="_ _20"> </span><span class="ff6">+<span class="_ _1e"> </span></span>B<span class="_ _24"></span>C<span class="_ _e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>D<span class="_ _24"></span>A<span class="ff6">,<span class="_ _c"> </span>demostraci´<span class="_ _d"></span>on</span></div><div class="t m0 xb2 h7 y1be ff6 fs3 fc0 sc0 ls0 ws0">Sean<span class="_ _c"> </span><span class="ff8">Q<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span></span>D<span class="_ _24"></span>P<span class="_ _29"> </span></span>;<span class="_ _c"> </span><span class="ffc">]<span class="ff8">D<span class="_ _24"></span>C<span class="_ _28"></span>Q<span class="_ _20"> </span></span></span>=<span class="_"> </span><span class="ffc">]<span class="ff8">P<span class="_ _29"> </span>C<span class="_ _28"></span>B<span class="_ _9"></span></span></span>,<span class="_ _c"> </span>tenemos:</div><div class="t m0 x53 h7 y1bf ffa fs3 fc0 sc0 ls0 ws0">4<span class="ff8">D<span class="_ _24"></span>C<span class="_ _9"></span>Q<span class="_ _20"> </span></span>∼<span class="_ _20"> </span>4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _f"> </span></span>⇒</div><div class="t m0 x60 h9 y1c0 ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>Q</div><div class="t m0 xd7 h9 y1c1 ff8 fs3 fc0 sc0 ls0 ws0">AB</div><div class="t m0 xd3 h7 y1bf ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xd8 h9 y1c0 ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _9"></span>Q</div><div class="t m0 xd8 h9 y1c1 ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>C</div><div class="t m0 xd9 h7 y1bf ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x28 h9 y1c0 ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>C</div><div class="t m0 xc9 h9 y1c1 ff8 fs3 fc0 sc0 ls0 ws0">AC</div><div class="t m0 xda h7 y1c2 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x70 hf y1c3 ffe fs3 fc0 sc0 ls0 ws0">○</div><div class="t m0 x53 h7 y1c4 ffa fs3 fc0 sc0 ls0 ws0">4<span class="ff8">D<span class="_ _24"></span>AC<span class="_ _c"> </span></span>∼<span class="_ _20"> </span>4<span class="ff8">B<span class="_ _9"></span>C<span class="_ _28"></span>Q<span class="_ _20"> </span></span>⇒</div><div class="t m0 x60 h9 y1c5 ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>A</div><div class="t m0 x60 h9 y1c6 ff8 fs3 fc0 sc0 ls0 ws0">QB</div><div class="t m0 xdb h7 y1c4 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xd8 h9 y1c5 ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>C</div><div class="t m0 xd8 h9 y1c6 ff8 fs3 fc0 sc0 ls0 ws0">QC</div><div class="t m0 xd9 h7 y1c4 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x28 h9 y1c5 ff8 fs3 fc0 sc0 ls0 ws0">AC</div><div class="t m0 x28 h9 y1c6 ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>C</div><div class="t m0 xda h7 y1c7 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x70 hf y1c8 ffe fs3 fc0 sc0 ls0 ws0">○</div><div class="t m0 xb9 h7 y1c9 ff6 fs3 fc0 sc0 ls0 ws0">de</div><div class="t m0 xdc h7 y1ca ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x4a hf y1cb ffe fs3 fc0 sc0 ls0 ws0">○</div><div class="t m0 xdd h7 y1c9 ff8 fs3 fc0 sc0 ls0 ws0">AB<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"></span></span>C<span class="_ _9"></span>D<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>D<span class="_ _24"></span>Q<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>AC</div><div class="t m0 xb9 h7 y1cc ff6 fs3 fc0 sc0 ls0 ws0">de</div><div class="t m0 xdc h7 y1cd ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4a hf y1ce ffe fs3 fc0 sc0 ls0 ws0">○</div><div class="t m0 xdd h7 y1cc ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>C<span class="_ _e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>D<span class="_ _24"></span>A<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>QB<span class="_ _20"> </span><span class="ffa">·<span class="_ _1e"> </span></span>AC</div><div class="t m0 xde hb y1cf ffb fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 xd8 h7 y1d0 ff6 fs3 fc0 sc0 ls0 ws0">sumando<span class="_ _c"> </span>obtenemos</div><div class="t m0 xdf h7 y1d1 ff6 fs3 fc0 sc0 ls0 ws0">lo<span class="_ _c"> </span>deseado</div><div class="t m0 xb h7 y1d2 ff6 fs3 fc0 sc0 ls0 ws0">nota:<span class="_ _13"> </span>Una<span class="_ _f"> </span>pincelada<span class="_ _13"> </span>muy<span class="_ _f"> </span>b<span class="_ _24"></span>onita<span class="_ _13"> </span>relacionada<span class="_ _f"> </span>con<span class="_ _13"> </span>esto<span class="_ _13"> </span>se<span class="_ _13"> </span>presen<span class="_ _3"></span>ta<span class="_ _13"> </span>de<span class="_ _13"> </span>la<span class="_ _f"> </span>siguiente<span class="_ _f"> </span>forma:</div><div class="t m0 xb h7 y1d3 ff6 fs3 fc0 sc0 ls0 ws0">Si<span class="_ _c"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _8"> </span></span></span>equil´<span class="_ _d"></span>atero<span class="_ _f"> </span>est´<span class="_ _d"></span>a<span class="_ _f"> </span>inscrito<span class="_ _c"> </span>en<span class="_ _c"> </span>una<span class="_ _f"> </span>circunferencia<span class="_ _c"> </span>y<span class="_ _f"> </span><span class="ff8">D<span class="_ _e"> </span><span class="ffa">∈</span></span></div><div class="t m0 xdb he y1d4 ffd fs4 fc0 sc0 ls0 ws0">_</div><div class="t m0 xe0 h7 y1d3 ff8 fs3 fc0 sc0 ls0 ws0">AC<span class="_ _f"> </span><span class="ff6">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _e"> </span><span class="ff8">AD<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>D<span class="_ _24"></span>C<span class="_ _f"> </span><span class="ff6">=<span class="_ _e"> </span></span>B<span class="_ _9"></span>D</span></span></span></div><div class="t m0 xb h7 y1d5 ff6 fs3 fc0 sc0 ls0 ws0">(T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Pompello)</div><div class="t m0 xa h7 y1d6 ff6 fs3 fc0 sc0 ls0 ws0">6,<span class="_ _c"> </span>7,<span class="_ _c"> </span>8<span class="_ _c"> </span>...<span class="_ _c"> </span>pueden<span class="_ _c"> </span>ser<span class="_ _c"> </span>sugerencias<span class="_ _c"> </span>de<span class="_ _f"> </span>n<span class="_ _3"></span>uestros<span class="_ _c"> </span>amigos.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">10</div><div class="t m0 xb h5 yc1 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#4<span class="_ _6"> </span>-<span class="_ _16"> </span>Otros<span class="_ _6"> </span>T<span class="_ _10"></span>eoremas</div><div class="t m0 xa h7 yc2 ff6 fs3 fc0 sc0 ls0 ws0">Estas<span class="_"> </span>notas<span class="_ _21"> </span>v<span class="_ _3"></span>an<span class="_"> </span>dirigidas<span class="_ _1e"> </span>may<span class="_ _3"></span>ormente<span class="_ _21"> </span>a<span class="_"> </span>estudian<span class="_ _3"></span>tes<span class="_"> </span>de<span class="_"> </span>Alto<span class="_ _1e"> </span>Rendimiento<span class="_ _21"> </span>que<span class="_"> </span>se<span class="_ _21"> </span>prepa-</div><div class="t m0 xb h7 yc3 ff6 fs3 fc0 sc0 ls0 ws0">ran<span class="_ _1e"> </span>con<span class="_"> </span>esmero<span class="_ _1e"> </span>para<span class="_ _1e"> </span>enfrentar<span class="_ _1e"> </span>las<span class="_ _21"> </span>diferen<span class="_ _3"></span>tes<span class="_"> </span>competencias<span class="_ _21"> </span>con<span class="_ _12"></span>v<span class="_ _3"></span>o<span class="_ _24"></span>cadas<span class="_"> </span>por<span class="_ _21"> </span>las<span class="_ _1e"> </span>matem´<span class="_ _a"></span>aticas.</div><div class="t m0 xa h7 y1d7 ff6 fs3 fc0 sc0 ls0 ws0">1<span class="_ _29"> </span><span class="ffa">·<span class="_ _1f"></span></span>-<span class="_ _13"> </span>En<span class="_ _8"> </span>to<span class="_ _24"></span>do<span class="_ _8"> </span><span class="ffa">4<span class="_ _13"> </span></span>se<span class="_ _8"> </span>cumple<span class="_ _13"> </span>que:<span class="_ _8"> </span><span class="ff8">a<span class="_ _20"> </span></span>+<span class="_"> </span><span class="ff8">b<span class="_ _8"> </span>><span class="_ _13"> </span>c</span>,<span class="_ _8"> </span><span class="ff8">b<span class="_ _20"> </span></span>+<span class="_"> </span><span class="ff8">c<span class="_ _8"> </span>><span class="_ _13"> </span>a</span>,<span class="_ _8"> </span><span class="ff8">c<span class="_ _20"> </span></span>+<span class="_"> </span><span class="ff8">a<span class="_ _13"> </span>><span class="_ _8"> </span>b<span class="_ _8"> </span><span class="ffa">−<span class="_ _2a"></span>→<span class="_ _8"> </span><span class="ff6">T<span class="_ _b"></span>eorema<span class="_ _13"> </span>de<span class="_ _8"> </span>la</span></span></span></div><div class="t m0 xb h7 y151 ff6 fs3 fc0 sc0 ls0 ws0">desigualdad<span class="_ _c"> </span>triangular.</div><div class="t m0 xa h7 y1d8 ff6 fs3 fc0 sc0 ls0 ws0">2<span class="_ _27"></span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _13"> </span>En<span class="_ _f"> </span>to<span class="_ _24"></span>do<span class="_ _f"> </span><span class="ffa">4<span class="_ _13"> </span></span>se<span class="_ _f"> </span>cumple<span class="_ _13"> </span>que:<span class="_ _f"> </span>el<span class="_ _13"> </span>segmen<span class="_ _3"></span>to<span class="_ _13"> </span>que<span class="_ _f"> </span>une<span class="_ _13"> </span>los<span class="_ _f"> </span>pun<span class="_ _12"></span>tos<span class="_ _f"> </span>medios<span class="_ _13"> </span>de<span class="_ _f"> </span>dos<span class="_ _13"> </span>de<span class="_ _f"> </span>sus</div><div class="t m0 xb h7 y1d9 ff6 fs3 fc0 sc0 ls0 ws0">lados<span class="_ _c"> </span>es<span class="_ _c"> </span>paralelo<span class="_ _c"> </span>al<span class="_ _c"> </span>tercero<span class="_ _c"> </span>y<span class="_ _c"> </span>mide<span class="_ _c"> </span>su<span class="_ _f"> </span>mitad<span class="_ _e"> </span><span class="ffa">−<span class="_ _4"></span>→<span class="_ _c"> </span><span class="ff6">T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>paralela<span class="_ _c"> </span>media<span class="_ _c"> </span>de<span class="_ _c"> </span>un<span class="_ _f"> </span><span class="ffa">4</span>.</span></span></div><div class="t m0 xa h7 y1da ff6 fs3 fc0 sc0 ls0 ws0">3<span class="_ _9"></span><span class="ffa">·<span class="_ _9"></span></span>-<span class="_ _c"> </span>Si<span class="_ _e"> </span>dos<span class="_ _c"> </span>bisectrices<span class="_ _e"> </span>de<span class="_ _c"> </span>un<span class="_ _e"> </span><span class="ffa">4<span class="_ _e"> </span></span>tienen<span class="_ _c"> </span>igual<span class="_ _e"> </span>longitud<span class="_ _c"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _e"> </span><span class="ff6">el<span class="_ _c"> </span></span>4<span class="_ _e"> </span><span class="ff6">es<span class="_ _c"> </span>is´<span class="_ _d"></span>osceles<span class="_ _c"> </span><span class="ffa">−<span class="_ _2a"></span>→<span class="_ _c"> </span><span class="ff6">T<span class="_ _b"></span>eorema</span></span></span></span></div><div class="t m0 xb h7 y1db ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>Steiner</div><div class="t m0 xa h7 y1dc ff6 fs3 fc0 sc0 ls0 ws0">4<span class="_ _27"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _f"> </span>La<span class="_ _f"> </span>suma<span class="_ _f"> </span>de<span class="_ _f"> </span>las<span class="_ _c"> </span>distancias<span class="_ _f"> </span>desde<span class="_ _f"> </span>un<span class="_ _f"> </span>punto<span class="_ _c"> </span>interior<span class="_ _c"> </span>de<span class="_ _f"> </span>un<span class="_ _f"> </span><span class="ffa">4<span class="_ _f"> </span></span>equil´<span class="_ _d"></span>atero<span class="_ _f"> </span>a<span class="_ _f"> </span>los<span class="_ _f"> </span>lados</div><div class="t m0 xb h7 y1dd ff6 fs3 fc0 sc0 ls0 ws0">del<span class="_ _c"> </span><span class="ffa">4<span class="_ _c"> </span></span>es<span class="_ _c"> </span>=<span class="_ _c"> </span>a<span class="_ _c"> </span>la<span class="_ _c"> </span>longitud<span class="_ _c"> </span>de<span class="_ _f"> </span>su<span class="_ _e"> </span>altura<span class="_ _c"> </span><span class="ffa">−<span class="_ _4"></span>→<span class="_ _c"> </span><span class="ff6">T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Viviani</span></span></div><div class="t m0 xa h7 y1de ff6 fs3 fc0 sc0 ls0 ws0">5<span class="_ _3"></span><span class="ffa">·<span class="_ _b"></span><span class="ff6">-<span class="_"> </span>Si<span class="_ _21"> </span>sobre<span class="_"> </span>los<span class="_ _1e"> </span>lados<span class="_"> </span><span class="ff8">AB<span class="_ _e"> </span></span>y<span class="_"> </span><span class="ff8">AC<span class="_ _e"> </span></span>de<span class="_"> </span>un<span class="_ _1e"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _c"> </span></span></span>se<span class="_"> </span>construy<span class="_ _3"></span>en,<span class="_"> </span>p<span class="_ _24"></span>or<span class="_"> </span>fuera,<span class="_ _1e"> </span>los<span class="_"> </span><span class="ffa">4<span class="_ _21"> </span></span>equil´<span class="_ _a"></span>ateros</span></span></div><div class="t m0 xb h9 y1df ff8 fs3 fc0 sc0 ls0 ws0">AB<span class="_ _24"></span>C</div><div class="t m0 x89 h8 y1e0 ff7 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 x21 h7 y1df ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">C<span class="_ _28"></span>AB</span></div><div class="t m0 xe2 h8 y1e0 ff7 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 x2 h7 y1df ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">B<span class="_ _9"></span>B</span></span></div><div class="t m0 x3 h8 y1e1 ff7 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 x9d h7 y1df ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">C<span class="_ _9"></span>C</span></div><div class="t m0 xb2 h8 y1e1 ff7 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 xa h7 y1e2 ff6 fs3 fc0 sc0 ls0 ws0">6<span class="_ _27"></span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _13"> </span>Si<span class="_ _f"> </span><span class="ff8">G<span class="_ _f"> </span></span>es<span class="_ _13"> </span>el<span class="_ _f"> </span>baricentro<span class="_ _f"> </span>de<span class="_ _f"> </span>un<span class="_ _13"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _24"></span>C<span class="_ _6"> </span></span></span>y<span class="_ _f"> </span>p<span class="_ _24"></span>or<span class="_ _13"> </span><span class="ff8">G<span class="_ _f"> </span></span>se<span class="_ _f"> </span>traza<span class="_ _13"> </span>una<span class="_ _f"> </span>recta<span class="_ _13"> </span>que<span class="_ _f"> </span>corte<span class="_ _f"> </span>a<span class="_ _13"> </span>los<span class="_ _f"> </span>3</div><div class="t m0 xb h7 y1e3 ff6 fs3 fc0 sc0 ls0 ws0">lados<span class="_ _13"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _f"> </span><span class="ff8">AX<span class="_ _c"> </span><span class="ff6">+<span class="_"> </span></span>B<span class="_ _24"></span>Z<span class="_ _6"> </span><span class="ff6">=<span class="_ _f"> </span></span>C<span class="_ _9"></span>Y<span class="_ _1e"> </span><span class="ff6">,<span class="_ _13"> </span>siendo<span class="_ _13"> </span></span>AX<span class="_ _28"></span><span class="ff6">,<span class="_ _13"> </span></span>B<span class="_ _24"></span>Z<span class="_ _6"> </span><span class="ff6">y<span class="_ _13"> </span></span>C<span class="_ _9"></span>Y<span class="_"> </span><span class="ff6">perp<span class="_ _24"></span>endiculares<span class="_ _13"> </span>desde<span class="_ _13"> </span></span>A<span class="ff6">,<span class="_ _f"> </span></span>B<span class="_ _9"></span><span class="ff6">,<span class="_ _13"> </span></span>C<span class="_ _6"> </span><span class="ff6">a<span class="_ _f"> </span>la</span></span></span></div><div class="t m0 xb h7 y1e4 ff6 fs3 fc0 sc0 ls0 ws0">recta.</div><div class="t m0 xa h7 y1e5 ff6 fs3 fc0 sc0 ls0 ws0">7<span class="ffa">·<span class="_ _3"></span><span class="ff6">-<span class="_"> </span>Las<span class="_ _20"> </span>proy<span class="_ _3"></span>ecciones<span class="_"> </span>de<span class="_"> </span>un<span class="_"> </span>punto<span class="_"> </span>de<span class="_"> </span>una<span class="_"> </span>circunferencia<span class="_"> </span>sobre<span class="_"> </span>los<span class="_"> </span>lados<span class="_"> </span>de<span class="_"> </span>un<span class="_"> </span><span class="ffa">4<span class="_ _20"> </span></span>inscrito</span></span></div><div class="t m0 xb h7 y1e6 ff6 fs3 fc0 sc0 ls0 ws0">en<span class="_ _c"> </span>dic<span class="_ _12"></span>ha<span class="_ _c"> </span>circunferencia<span class="_ _c"> </span>determinan<span class="_ _c"> </span>una<span class="_ _c"> </span>recta<span class="_ _c"> </span><span class="ffa">−<span class="_ _2a"></span>→<span class="_ _f"> </span><span class="ff6">Recta<span class="_ _e"> </span>de<span class="_ _c"> </span>Simpson.</span></span></div><div class="t m0 xa h7 y1e7 ff6 fs3 fc0 sc0 ls0 ws0">8<span class="_ _27"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _f"> </span>Circunferencia<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _f"> </span>9<span class="_ _c"> </span>puntos<span class="_ _c"> </span><span class="ffa">−<span class="_ _2a"></span>→<span class="_ _f"> </span><span class="ff6">Es<span class="_ _f"> </span>la<span class="_ _c"> </span>que<span class="_ _f"> </span>pasa<span class="_ _f"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>los<span class="_ _c"> </span>puntos<span class="_ _c"> </span>medios<span class="_ _f"> </span>de<span class="_ _f"> </span>cada</span></span></div><div class="t m0 xb h7 y1e8 ff6 fs3 fc0 sc0 ls0 ws0">lado,<span class="_ _c"> </span>los<span class="_ _c"> </span>pies<span class="_ _c"> </span>de<span class="_ _c"> </span>las<span class="_ _f"> </span>alturas<span class="_ _e"> </span>y<span class="_ _f"> </span>los<span class="_ _e"> </span>puntos<span class="_ _c"> </span>medios<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>segmentos<span class="_ _e"> </span>que<span class="_ _f"> </span>unen<span class="_ _e"> </span>los<span class="_ _f"> </span>v<span class="_ _3"></span>´<span class="_ _a"></span>ertices<span class="_ _f"> </span>al</div><div class="t m0 xb h7 y1e9 ff6 fs3 fc0 sc0 ls0 ws0">orto<span class="_ _24"></span>cen<span class="_ _3"></span>tro<span class="_ _e"> </span>de<span class="_ _e"> </span>un<span class="_"> </span><span class="ffa">4</span>.<span class="_ _e"> </span>El<span class="_ _e"> </span>cen<span class="_ _12"></span>tro<span class="_"> </span>de<span class="_ _e"> </span>esta<span class="_ _e"> </span>circunferencia<span class="_"> </span>es<span class="_ _e"> </span>el<span class="_ _e"> </span>pun<span class="_ _12"></span>to<span class="_"> </span>medio<span class="_ _e"> </span>desde<span class="_ _e"> </span>el<span class="_"> </span>orto<span class="_ _24"></span>centro</div><div class="t m0 xb h7 y1ea ff6 fs3 fc0 sc0 ls0 ws0">al<span class="_ _c"> </span>cen<span class="_ _12"></span>tro<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>circunferencia<span class="_ _c"> </span>circunscrita.</div><div class="t m0 xa h7 y1eb ff6 fs3 fc0 sc0 ls0 ws0">9<span class="_ _27"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _f"> </span>T<span class="_ _10"></span>ri´<span class="_ _a"></span>angulo<span class="_ _c"> </span>p<span class="_ _24"></span>edal<span class="_ _f"> </span><span class="ffa">−<span class="_ _2a"></span>→<span class="_ _f"> </span><span class="ff6">Es<span class="_ _f"> </span>el<span class="_ _f"> </span></span>4<span class="_ _c"> </span><span class="ff6">determinado<span class="_ _f"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>los<span class="_ _f"> </span>pies<span class="_ _c"> </span>de<span class="_ _f"> </span>las<span class="_ _f"> </span>alturas<span class="_ _c"> </span>de<span class="_ _f"> </span>un<span class="_ _f"> </span></span>4<span class="ff6">.<span class="_ _f"> </span>El</span></span></div><div class="t m0 xb h7 y1ec ff6 fs3 fc0 sc0 ls0 ws0">orto<span class="_ _24"></span>cen<span class="_ _3"></span>tro<span class="_ _f"> </span>del<span class="_ _e"> </span><span class="ffa">4<span class="_ _c"> </span></span>coincide<span class="_ _c"> </span>con<span class="_ _f"> </span>el<span class="_ _e"> </span>incentro<span class="_ _e"> </span>del<span class="_ _c"> </span><span class="ffa">4<span class="_ _f"> </span></span>pedal.</div><div class="t m0 xa h7 y1ed ff6 fs3 fc0 sc0 ls0 ws0">10<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Stewart:<span class="_ _e"> </span>Sea<span class="_ _c"> </span><span class="ff8">AD<span class="_ _f"> </span></span>una<span class="_ _c"> </span>ceviana<span class="_ _c"> </span>cualquiera...</div><div class="t m0 x7b h9 y1ee ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xe3 h9 y1ef ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x22 h9 y1f0 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xd1 h9 y1f1 ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x7 h9 y1f2 ff8 fs3 fc0 sc0 ls0 ws0">AB</div><div class="t m0 x54 ha y1f3 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe4 h7 y1f2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _28"></span><span class="ff8">D<span class="_ _24"></span>C<span class="_ _33"> </span><span class="ff6">+<span class="_ _28"></span></span>AC</span></div><div class="t m0 x23 ha y1f3 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe5 h7 y1f2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _28"></span><span class="ff8">B<span class="_ _9"></span>D<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>AD</span></div><div class="t m0 x91 ha y1f3 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe6 h7 y1f2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _28"></span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _1f"> </span><span class="ff6">+<span class="_ _27"></span></span>B<span class="_ _9"></span>D<span class="_ _29"> </span></span>·<span class="_ _27"></span><span class="ff8">D<span class="_ _24"></span>C<span class="_ _1f"> </span></span>·<span class="_ _28"></span><span class="ff8">B<span class="_ _9"></span>C</span></div><div class="t m0 x7 h7 y1f4 ff6 fs3 fc0 sc0 ls0 ws0">P<span class="_ _3"></span>ara<span class="_ _13"> </span>su<span class="_ _13"> </span>demostraci´<span class="_ _d"></span>on,<span class="_ _13"> </span>trace<span class="_ _13"> </span>la<span class="_ _13"> </span>altura<span class="_ _13"> </span>desde<span class="_ _f"> </span><span class="ff8">A<span class="_ _13"> </span></span>y</div><div class="t m0 x7 h7 y1f5 ff6 fs3 fc0 sc0 ls0 ws0">aplique<span class="_ _c"> </span>reiteradas<span class="_ _c"> </span>veces<span class="_ _e"> </span>el<span class="_ _c"> </span>teorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Pit´<span class="_ _a"></span>agoras</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">11</div><div class="t m0 xa h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">11<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _c"> </span>bisectriz<span class="_ _c"> </span>interior<span class="_ _e"> </span>y<span class="_ _c"> </span>exterior<span class="_ _f"> </span>de<span class="_ _e"> </span>un<span class="_ _c"> </span><span class="ffa">4</span></div><div class="t m0 x7b h9 y1f6 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 y1f7 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x2d h9 y1f8 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xa4 h9 y1f9 ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x69 h7 y1fa ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 x80 h7 y1fb ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xe7 h9 y1fc ff8 fs3 fc0 sc0 ls0 ws0">AB</div><div class="t m0 xe7 h9 y1fd ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>C</div><div class="t m0 x9f h7 y1fe ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 x4a h9 y1fc ff8 fs3 fc0 sc0 ls0 ws0">AD</div><div class="t m0 x4a h9 y1fd ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _24"></span>C</div><div class="t m0 x3e h9 y1ff ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xe8 h9 y200 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 xe9 h9 y201 ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _34"> </span>D</div><div class="t m0 x1a h7 y202 ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xea h7 y203 ffa fs3 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xa h7 y204 ff6 fs3 fc0 sc0 ls0 ws0">12<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Cev<span class="_ _3"></span>a<span class="_ _c"> </span>y<span class="_ _c"> </span>Menelao</div><div class="t m0 x7b h9 y205 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x36 h9 y206 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x2d h9 y207 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 xeb h9 y208 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x2e h9 y209 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xb0 h9 y20a ff8 fs3 fc0 sc0 ls0 ws0">R</div><div class="t m0 xb3 h9 y20b ff8 fs3 fc0 sc0 ls0 ws0">AR</div><div class="t m0 xb3 h9 y20c ff8 fs3 fc0 sc0 ls0 ws0">RB</div><div class="t m0 x39 h7 y20d ffa fs3 fc0 sc0 ls0 ws0">·</div><div class="t m0 xec h9 y20b ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>P</div><div class="t m0 xec h9 y20c ff8 fs3 fc0 sc0 ls0 ws0">P<span class="_ _29"> </span>C</div><div class="t m0 xdd h7 y20d ffa fs3 fc0 sc0 ls0 ws0">·</div><div class="t m0 xed h9 y20b ff8 fs3 fc0 sc0 ls0 ws0">C<span class="_ _9"></span>Q</div><div class="t m0 xed h9 y20c ff8 fs3 fc0 sc0 ls0 ws0">QA</div><div class="t m0 xe4 h7 y20d ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>1</div><div class="t m0 x5d h9 y20e ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xee h9 y20f ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x24 h9 y210 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 xef h9 y211 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 xc3 h9 y212 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x93 h9 y213 ff8 fs3 fc0 sc0 ls0 ws0">R</div><div class="t m0 xa h7 y214 ff6 fs3 fc0 sc0 ls0 ws0">13<span class="_ _29"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _13"> </span>T<span class="_ _10"></span>eorema<span class="_ _13"> </span>de<span class="_ _13"> </span>P<span class="_ _3"></span>ascal:<span class="_ _13"> </span>En<span class="_ _13"> </span>to<span class="_ _24"></span>do<span class="_ _13"> </span>hex´<span class="_ _d"></span>agono<span class="_ _13"> </span>inscriptible<span class="_ _13"> </span>sin<span class="_ _f"> </span>lados<span class="_ _13"> </span>opuestos<span class="_ _13"> </span>paralelos,</div><div class="t m0 xb h7 y215 ff6 fs3 fc0 sc0 ls0 ws0">las<span class="_ _c"> </span>in<span class="_ _12"></span>tersecciones<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="_ _c"> </span>opuestos<span class="_ _c"> </span>determinan<span class="_ _c"> </span>3<span class="_ _c"> </span>puntos<span class="_ _e"> </span>alineados</div><div class="t m0 xa h7 y216 ff6 fs3 fc0 sc0 ls0 ws0">14<span class="ffa">·<span class="_ _12"></span><span class="ff6">-<span class="_"> </span>Desigualdad<span class="_"> </span>de<span class="_"> </span>Euler:<span class="_"> </span><span class="ff8">R<span class="_ _20"> </span><span class="ffa">≥<span class="_ _20"> </span></span></span>2<span class="ff8">r<span class="_ _e"> </span></span>con<span class="_"> </span>igualdad<span class="_ _20"> </span>si<span class="_ _20"> </span>el<span class="_ _20"> </span><span class="ffa">4<span class="_ _20"> </span></span>es<span class="_"> </span>equil´<span class="_ _a"></span>atero.<span class="_"> </span><span class="ff8">R<span class="_ _20"> </span><span class="ffa">→<span class="_ _20"> </span></span></span>circunradio,</span></span></div><div class="t m0 xb h7 y217 ff8 fs3 fc0 sc0 ls0 ws0">r<span class="_ _e"> </span><span class="ffa">→<span class="_ _c"> </span><span class="ff6">inradio</span></span></div><div class="t m0 xa h7 y218 ff6 fs3 fc0 sc0 ls0 ws0">15<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>C´<span class="_ _d"></span>alculo<span class="_ _f"> </span>de<span class="_ _e"> </span>´<span class="_ _a"></span>areas:</div><div class="t m0 x7f h7 y219 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">4<span class="_ _e"> </span></span>:<span class="_ _c"> </span><span class="ff8">A<span class="_ _20"> </span></span>=</div><div class="t m0 x4e h7 y21a ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>h</div><div class="t m0 xa5 h7 y21b ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa6 h7 y219 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xac h7 y21a ff8 fs3 fc0 sc0 ls0 ws0">a<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>b<span class="_ _1f"> </span><span class="ff6">sen<span class="_ _1f"> </span></span>γ</div><div class="t m0 xd5 h7 y21b ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf0 h7 y219 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">ρr<span class="_ _e"> </span></span>=</div><div class="t m0 xdd h9 y21a ff8 fs3 fc0 sc0 ls0 ws0">abc</div><div class="t m0 xdd h7 y21b ff6 fs3 fc0 sc0 ls0 ws0">4<span class="ff8">R</span></div><div class="t m0 x71 h7 y219 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xf1 hb y21c ffb fs3 fc0 sc0 ls0 ws0">p</div><div class="t m0 x5c h7 y219 ff8 fs3 fc0 sc0 ls0 ws0">ρ<span class="ff6">(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>b<span class="ff6">)(</span>ρ<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>c<span class="ff6">)<span class="_ _c"> </span>(Her´<span class="_ _d"></span>on)</span></div><div class="t m0 x5f h7 y21d ff8 fs3 fc0 sc0 ls0 ws0">a<span class="ff6">,<span class="_ _c"> </span></span>b<span class="ff6">,<span class="_ _c"> </span></span>c<span class="_ _c"> </span><span class="ff6">lados<span class="_ _c"> </span>del<span class="_ _c"> </span><span class="ffa">4</span>,<span class="_ _c"> </span></span>h<span class="_ _20"> </span><span class="ffa">→<span class="_ _c"> </span><span class="ff6">altura<span class="_ _c"> </span>del<span class="_ _f"> </span>lado<span class="_ _e"> </span></span></span>b</div><div class="t m0 x5f h7 y21e ff8 fs3 fc0 sc0 ls0 ws0">γ<span class="_ _c"> </span><span class="ffa">→<span class="_ _c"> </span><span class="ff6">´<span class="_ _d"></span>angulo<span class="_ _f"> </span>opuesto<span class="_ _e"> </span>al<span class="_ _c"> </span>lado<span class="_ _f"> </span><span class="ff8">c</span></span></span></div><div class="t m0 x5f h7 y21f ff8 fs3 fc0 sc0 ls0 ws0">ρ<span class="_ _20"> </span><span class="ffa">→<span class="_ _c"> </span><span class="ff6">semip<span class="_ _24"></span>er<span class="_ _10"></span>´<span class="_ _11"></span>ımetro<span class="_ _c"> </span>del<span class="_ _c"> </span><span class="ffa">4</span></span></span></div><div class="t m0 x7f h7 y220 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Cuadril´<span class="_ _d"></span>atero:<span class="_ _c"> </span><span class="ff8">A<span class="_ _20"> </span></span>=</div><div class="t m0 xf2 h9 y221 ff8 fs3 fc0 sc0 ls0 ws0">d</div><div class="t m0 x8d ha y222 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xae h7 y221 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff8">d</span></div><div class="t m0 xf3 ha y222 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf4 h7 y223 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb4 h7 y220 ff6 fs3 fc0 sc0 ls0 ws0">sen<span class="_ _1f"> </span><span class="ff8">σ</span></div><div class="t m0 x5f h9 y224 ff8 fs3 fc0 sc0 ls0 ws0">d</div><div class="t m0 x5a ha y225 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xeb h7 y224 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">d</span></div><div class="t m0 x7d ha y225 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2b h7 y224 ffa fs3 fc0 sc0 ls0 ws0">→<span class="_ _c"> </span><span class="ff6">diagonales,<span class="_ _35"> </span><span class="ff8">σ<span class="_ _e"> </span></span></span>→<span class="_ _20"> </span><span class="ffc">]<span class="_ _c"> </span><span class="ff6">formado<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>las<span class="_ _c"> </span>diagonales</span></span></div><div class="t m0 xa h7 y226 ff6 fs3 fc0 sc0 ls0 ws0">16<span class="_ _27"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _f"> </span>En<span class="_ _f"> </span>to<span class="_ _24"></span>do<span class="_ _f"> </span>paralelogramo<span class="_ _f"> </span>la<span class="_ _f"> </span>suma<span class="_ _f"> </span>de<span class="_ _f"> </span>los<span class="_ _c"> </span>cuadrados<span class="_ _f"> </span>de<span class="_ _f"> </span>sus<span class="_ _f"> </span>lados<span class="_ _f"> </span>multiplicados<span class="_ _c"> </span>p<span class="_ _24"></span>or</div><div class="t m0 xb h7 y227 ff6 fs3 fc0 sc0 ls0 ws0">dos<span class="_ _c"> </span>es<span class="_ _c"> </span>=<span class="_ _c"> </span>a<span class="_ _c"> </span>la<span class="_ _c"> </span>suma<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _f"> </span>cuadrados<span class="_ _e"> </span>de<span class="_ _c"> </span>sus<span class="_ _f"> </span>diagonales.</div><div class="t m0 xa h7 y228 ff6 fs3 fc0 sc0 ls0 ws0">17<span class="ffa">·</span>-<span class="_"> </span>T<span class="_ _10"></span>eorema<span class="_ _e"> </span>de<span class="_"> </span>V<span class="_ _b"></span>arignon:<span class="_"> </span>Al<span class="_"> </span>unir<span class="_ _20"> </span>los<span class="_ _e"> </span>4<span class="_"> </span>puntos<span class="_"> </span>medios<span class="_"> </span>de<span class="_"> </span>cada<span class="_"> </span>lado<span class="_"> </span>de<span class="_"> </span>un<span class="_ _20"> </span>cuadril´<span class="_ _a"></span>atero</div><div class="t m0 xb h7 y229 ff6 fs3 fc0 sc0 ls0 ws0">se<span class="_ _c"> </span>obtiene<span class="_ _c"> </span>un<span class="_ _c"> </span>paralelogramo.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">12</div><div class="t m0 x38 h10 y9 fff fs3 fc0 sc0 ls0 ws0">Algunos<span class="_ _16"> </span>lemas<span class="_ _2f"> </span>necesarios</div><div class="t m0 xa h7 ya ff6 fs3 fc0 sc0 ls0 ws0">18<span class="_ _29"> </span><span class="ffa">·<span class="_ _1f"></span></span>-<span class="_ _13"> </span>La<span class="_ _8"> </span>distancia<span class="_ _8"> </span>del<span class="_ _13"> </span>circuncentro<span class="_ _13"> </span>a<span class="_ _8"> </span>uno<span class="_ _13"> </span>de<span class="_ _8"> </span>los<span class="_ _13"> </span>lados<span class="_ _8"> </span>de<span class="_ _8"> </span>un<span class="_ _13"> </span><span class="ffa">4<span class="_ _8"> </span></span>tiene<span class="_ _8"> </span>la<span class="_ _13"> </span>mitad<span class="_ _8"> </span>de<span class="_ _8"> </span>la</div><div class="t m0 xb h7 yb ff6 fs3 fc0 sc0 ls0 ws0">longitud<span class="_ _c"> </span>del<span class="_ _c"> </span>segmento<span class="_ _e"> </span>que<span class="_ _c"> </span>une<span class="_ _c"> </span>al<span class="_ _c"> </span>orto<span class="_ _24"></span>centro<span class="_ _e"> </span>del<span class="_ _c"> </span><span class="ffa">4<span class="_ _c"> </span></span>con<span class="_ _f"> </span>el<span class="_ _e"> </span>v´<span class="_ _a"></span>ertice<span class="_ _c"> </span>opuesto<span class="_ _c"> </span>al<span class="_ _c"> </span>lado.</div><div class="t m0 xa h7 y22a ff6 fs3 fc0 sc0 ls0 ws0">19<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Si<span class="_ _c"> </span><span class="ff8">AB<span class="_ _c"> </span><span class="ffa">⊥<span class="_ _20"> </span></span>C<span class="_ _28"></span>D<span class="_ _f"> </span></span>en<span class="_ _e"> </span><span class="ff8">N<span class="_ _13"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">AC</span></span></div><div class="t m0 x39 ha y22b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6 h7 y22a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">AD</span></div><div class="t m0 x8c ha y22b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf5 h7 y22a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">B<span class="_ _24"></span>C</span></div><div class="t m0 x66 ha y22b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x57 h7 y22a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">B<span class="_ _24"></span>D</span></div><div class="t m0 xf6 ha y22b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">20<span class="_ _9"></span><span class="ffa">·<span class="_ _28"></span></span>-<span class="_ _c"> </span>Si<span class="_ _e"> </span><span class="ff8">AA</span></div><div class="t m0 x9a ha y22d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xf7 h7 y22c ffa fs3 fc0 sc0 ls0 ws0">⊥<span class="_ _20"> </span><span class="ff8">B<span class="_ _24"></span>B</span></div><div class="t m0 x20 ha y22d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xf8 h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 xf9 ha y22e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb5 h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _33"> </span><span class="ff8">b</span></div><div class="t m0 x9f ha y22e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa0 h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>5<span class="ff8">c</span></div><div class="t m0 x62 ha y22e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xfa h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _e"> </span>con<span class="_ _c"> </span><span class="ff8">AA</span></div><div class="t m0 xbe ha y22d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xfb h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">mediana<span class="_ _e"> </span>de<span class="_ _c"> </span><span class="ff8">a<span class="_ _e"> </span></span>y<span class="_ _c"> </span><span class="ff8">B<span class="_ _9"></span>B</span></div><div class="t m0 xfc ha y22d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xfd h7 y22c ff6 fs3 fc0 sc0 ls0 ws0">mediana<span class="_ _e"> </span>de<span class="_ _c"> </span><span class="ff8">b<span class="_ _e"> </span></span>en</div><div class="t m0 xb h7 y22f ff6 fs3 fc0 sc0 ls0 ws0">un<span class="_ _c"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _13"> </span></span></span>(Esto<span class="_ _c"> </span>se<span class="_ _c"> </span>prueba<span class="_ _c"> </span>aplicando<span class="_ _c"> </span>19)</div><div class="t m0 xa h7 y230 ff6 fs3 fc0 sc0 ls0 ws0">21<span class="_ _1f"> </span><span class="ffa">·<span class="_ _29"></span></span>-<span class="_ _8"> </span>Lema<span class="_ _36"> </span>de<span class="_ _8"> </span>Ra<span class="_ _12"></span>v<span class="_ _10"></span>´<span class="_ _11"></span>ı:<span class="_ _8"> </span>En<span class="_ _8"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _28"></span></span></span>,<span class="_ _8"> </span><span class="ff8">I<span class="_ _16"> </span></span>es<span class="_ _8"> </span>el<span class="_ _8"> </span>incen<span class="_ _12"></span>tro,<span class="_ _8"> </span><span class="ff8">P<span class="_ _29"> </span></span>,<span class="_ _8"> </span><span class="ff8">Q</span>,<span class="_ _8"> </span><span class="ff8">R<span class="_ _36"> </span></span>pun<span class="_ _12"></span>tos<span class="_ _8"> </span>de<span class="_ _8"> </span>tangencia<span class="_ _8"> </span>del</div><div class="t m0 xb h7 y231 ff6 fs3 fc0 sc0 ls0 ws0">inc<span class="_ _10"></span>´<span class="_ _11"></span>ırculo<span class="_ _c"> </span>con<span class="_ _c"> </span>los<span class="_ _c"> </span>lados<span class="_ _c"> </span>del<span class="_ _c"> </span><span class="ffa">4<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒</span></div><div class="t m0 x7b h9 y232 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x35 h9 y233 ff8 fs3 fc0 sc0 ls0 ws0">C</div><div class="t m0 x22 h9 y234 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x31 h9 y235 ff8 fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xa8 h9 y236 ff8 fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x11 h9 y237 ff8 fs3 fc0 sc0 ls0 ws0">R</div><div class="t m0 x30 h9 y238 ff8 fs3 fc0 sc0 ls0 ws0">I</div><div class="t m0 xfe h9 y239 ff8 fs3 fc0 sc0 ls0 ws0">y</div><div class="t m0 xff h9 y23a ff8 fs3 fc0 sc0 ls0 ws0">y</div><div class="t m0 x69 h9 y23b ff8 fs3 fc0 sc0 ls0 ws0">m</div><div class="t m0 xa6 h9 y23c ff8 fs3 fc0 sc0 ls0 ws0">m</div><div class="t m0 x76 h9 y23d ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x4d h9 y23e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xec h7 y23f ff8 fs3 fc0 sc0 ls0 ws0">AR<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>AQ<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>x<span class="ff6">,<span class="_ _c"> </span></span>B<span class="_ _9"></span>R<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>B<span class="_ _9"></span>P<span class="_ _13"> </span><span class="ff6">=<span class="_"> </span></span>y<span class="_ _9"></span><span class="ff6">,<span class="_ _c"> </span></span>C<span class="_ _28"></span>P<span class="_ _13"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _28"></span>Q<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>m</div><div class="t m0 xec h7 y240 ffc fs3 fc0 sc0 ls0 ws0">∴<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>y<span class="_ _21"> </span><span class="ff6">+<span class="_ _1e"> </span></span>m<span class="ff6">,<span class="_ _c"> </span></span>b<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>m<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>x<span class="ff6">,<span class="_ _c"> </span></span>c<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>x<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>y</span></div><div class="t m0 xec h7 y241 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">m<span class="_ _20"> </span><span class="ff6">=</span></span></span></div><div class="t m0 x72 h7 y242 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x72 h7 y243 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x100 h7 y241 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a<span class="_ _1f"> </span></span>+<span class="_ _33"> </span><span class="ff8">b<span class="_ _33"> </span><span class="ffa">−<span class="_ _33"></span></span>c</span>),<span class="_ _e"> </span><span class="ff8">y<span class="_ _c"> </span></span>=</div><div class="t m0 xca h7 y242 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 xca h7 y243 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 x101 h7 y241 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">c<span class="_ _1f"> </span></span>+<span class="_ _33"> </span><span class="ff8">b<span class="_ _33"> </span><span class="ffa">−<span class="_ _33"></span></span>b</span>),<span class="_ _e"> </span><span class="ff8">x<span class="_ _20"> </span></span>=</div><div class="t m0 x102 h7 y242 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a</div><div class="t m0 x93 h7 y243 ff6 fs3 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa h7 y244 ff6 fs3 fc0 sc0 ls0 ws0">22<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-</div><div class="t m0 x7b h9 y245 ff8 fs3 fc0 sc0 ls0 ws0">T</div><div class="t m0 x3d h9 y246 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x103 h9 y247 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x104 h9 y248 ff8 fs3 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x105 h7 y245 ff6 fs3 fc0 sc0 ls0 ws0">Γ</div><div class="t m0 x106 h9 y249 ff8 fs3 fc0 sc0 ls0 ws0">E</div><div class="t m0 x7d h9 y24a ff8 fs3 fc0 sc0 ls0 ws0">F</div><div class="t m0 xb1 h9 y24b ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x35 ha y24c ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x107 h9 y24d ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x3a ha y24e ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xb6 h7 y24f ff6 fs3 fc0 sc0 ls0 ws0">Si<span class="_ _e"> </span><span class="ff8">ω<span class="_ _f"> </span></span>y<span class="_ _c"> </span>Γ<span class="_ _c"> </span>son<span class="_ _e"> </span>dos<span class="_ _c"> </span>circunferencias<span class="_ _c"> </span>tangentes<span class="_ _20"> </span>in-</div><div class="t m0 xb6 h7 y250 ff6 fs3 fc0 sc0 ls0 ws0">ternas<span class="_ _c"> </span>en<span class="_ _c"> </span><span class="ff8">T<span class="_ _29"> </span></span>;<span class="_ _c"> </span><span class="ff8">A<span class="_ _c"> </span></span>y<span class="_ _f"> </span><span class="ff8">B<span class="_ _f"> </span></span>son<span class="_ _c"> </span>puntos<span class="_ _e"> </span>de<span class="_ _c"> </span>Γ,</div><div class="t m0 xb6 h9 y251 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 xe4 ha y252 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x99 h7 y251 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">T<span class="_ _29"> </span>A</span></div><div class="t m0 xba hb y253 ffb fs3 fc0 sc0 ls0 ws0">T</div><div class="t m0 xc8 h7 y251 ff8 fs3 fc0 sc0 ls0 ws0">ω<span class="_ _f"> </span><span class="ff6">y<span class="_ _c"> </span></span>B</div><div class="t m0 xd4 ha y252 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xca h7 y251 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">T<span class="_ _29"> </span>B</span></div><div class="t m0 xea hb y253 ffb fs3 fc0 sc0 ls0 ws0">T</div><div class="t m0 x108 h7 y251 ff6 fs3 fc0 sc0 ls0 ws0">Γ<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒</span></div><div class="t m0 x99 h9 y254 ff8 fs3 fc0 sc0 ls0 ws0">T<span class="_ _29"> </span>A</div><div class="t m0 x99 h9 y255 ff8 fs3 fc0 sc0 ls0 ws0">T<span class="_ _29"> </span>B</div><div class="t m0 x109 h7 y256 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xa9 h9 y254 ff8 fs3 fc0 sc0 ls0 ws0">AE</div><div class="t m0 xa9 h9 y255 ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>F</div><div class="t m0 xf6 h7 y256 ff6 fs3 fc0 sc0 ls0 ws0">siendo<span class="_"> </span><span class="ff8">AE<span class="_ _c"> </span></span>y<span class="_ _20"> </span><span class="ff8">B<span class="_ _9"></span>F<span class="_ _8"> </span></span>tangentes<span class="_"> </span>a<span class="_"> </span><span class="ff8">ω</span></div><div class="t m0 xb6 h7 y257 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _c"> </span>V<span class="_ _b"></span>ea<span class="_ _c"> </span>que<span class="_ _c"> </span><span class="ff8">A</span></div><div class="t m0 xc8 ha y258 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x10a h9 y257 ff8 fs3 fc0 sc0 ls0 ws0">B</div><div class="t m0 x10b ha y258 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x10c h7 y257 ffa fs3 fc0 sc0 ls0 ws0">k<span class="_ _20"> </span><span class="ff8">AB</span></div><div class="t m0 xb6 h7 y259 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>p<span class="_ _24"></span>otencia<span class="_ _c"> </span>de<span class="_ _c"> </span>un<span class="_ _c"> </span>punto</div><div class="t m0 x10d h9 y25a ff8 fs3 fc0 sc0 ls0 ws0">AE</div><div class="t m0 x10e ha y25b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10f h7 y25a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">AA</span></div><div class="t m0 xc7 ha y25c ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x24 h7 y25a ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff8">AT</span></div><div class="t m0 x10d h9 y25d ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _24"></span>F</div><div class="t m0 x10e ha y25e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10f h7 y25d ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">B<span class="_ _24"></span>B</span></div><div class="t m0 xc7 ha y25f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x24 h7 y25d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff8">B<span class="_ _24"></span>T<span class="_ _1f"> </span><span class="ff6">,<span class="_ _e"> </span>etc<span class="_ _f"> </span>...</span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">13</div><div class="t m0 xa h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">23<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-</div><div class="t m0 xe7 h9 y260 ff8 fs3 fc0 sc0 ls0 ws0">A</div><div class="t m0 x41 h9 y261 ff8 fs3 fc0 sc0 ls0 ws0">B<span class="_ _37"> </span>C</div><div class="t m0 x68 h9 y97 ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x3d h9 y262 ff8 fs3 fc0 sc0 ls0 ws0">E</div><div class="t m0 x2e h9 y263 ff8 fs3 fc0 sc0 ls0 ws0">F</div><div class="t m0 x3a h9 y97 ff8 fs3 fc0 sc0 ls0 ws0">X</div><div class="t m0 xcd h9 y264 ff8 fs3 fc0 sc0 ls0 ws0">Y</div><div class="t m0 xfe h9 y265 ff8 fs3 fc0 sc0 ls0 ws0">Z</div><div class="t m0 xe7 h9 y266 ff8 fs3 fc0 sc0 ls0 ws0">T</div><div class="t m0 xe7 h9 y267 ff8 fs3 fc0 sc0 ls0 ws0">σ</div><div class="t m0 x6b h9 y268 ff8 fs3 fc0 sc0 ls0 ws0">σ</div><div class="t m0 x3b he y269 ffd fs4 fc0 sc0 ls0 ws0">a</div><div class="t m0 x110 h7 y26a ff6 fs3 fc0 sc0 ls0 ws0">Si<span class="_ _38"> </span><span class="ff8">D<span class="_ _24"></span></span>,<span class="_ _38"> </span><span class="ff8">E<span class="_ _9"></span></span>,<span class="_ _38"> </span><span class="ff8">F<span class="_ _19"> </span></span>pun<span class="_ _3"></span>tos<span class="_ _38"> </span>de<span class="_ _38"> </span>tangencia<span class="_ _38"> </span>del</div><div class="t m0 x110 h7 y26b ff6 fs3 fc0 sc0 ls0 ws0">inc<span class="_ _10"></span>´<span class="_ _11"></span>ırculo<span class="_ _f"> </span>de<span class="_ _f"> </span>cen<span class="_ _12"></span>tro<span class="_ _f"> </span><span class="ff8">σ<span class="_ _13"> </span></span>en<span class="_ _f"> </span><span class="ffa">4<span class="ff8">AB<span class="_ _9"></span>C<span class="_ _28"></span></span></span>.<span class="_ _f"> </span>Si<span class="_ _f"> </span><span class="ff8">D<span class="_ _24"></span>T</span></div><div class="t m0 x110 h7 y26c ff6 fs3 fc0 sc0 ls0 ws0">es<span class="_ _2e"> </span>di´<span class="_ _d"></span>ametro;<span class="_ _2e"> </span>recta</div><div class="t m0 x111 h7 y26d ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _39"></span>→</div><div class="t m0 x111 h7 y26c ff8 fs3 fc0 sc0 ls0 ws0">AT<span class="_ _1d"> </span><span class="ff6">corta<span class="_ _2e"> </span></span>B<span class="_ _24"></span>C<span class="_ _19"> </span><span class="ff6">en</span></div><div class="t m0 x110 h7 y26e ff8 fs3 fc0 sc0 ls0 ws0">X<span class="_ _f"> </span><span class="ff6">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">B<span class="_ _24"></span>D<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>C<span class="_ _28"></span>X</span></span></span></div><div class="t m0 x110 h7 y26f ff6 fs3 fc0 sc0 ls0 ws0">Demostraci´<span class="_ _d"></span>on:</div><div class="t m0 x110 h7 y270 ff6 fs3 fc0 sc0 ls0 ws0">2<span class="ff8">B<span class="_ _24"></span>D<span class="_ _e"> </span></span>=<span class="_"> </span><span class="ff8">B<span class="_ _9"></span>C<span class="_ _e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">AB<span class="_ _20"> </span><span class="ffa">−<span class="_ _1e"> </span></span>AC<span class="_ _13"> </span></span>p<span class="_ _24"></span>or<span class="_ _c"> </span>21)</div><div class="t m0 x110 h7 y271 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">B<span class="_ _24"></span>F<span class="_ _f"> </span></span>+<span class="_ _1e"> </span><span class="ff8">B<span class="_ _9"></span>Z<span class="_ _e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _28"></span>D</span></div><div class="t m0 x110 h7 y272 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">F<span class="_ _29"> </span>Z<span class="_ _20"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _28"></span>D<span class="_ _e"> </span></span>=<span class="_"> </span><span class="ff8">E<span class="_ _28"></span>Y<span class="_ _8"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _27"></span>D</span></div><div class="t m0 x110 h7 y273 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">E<span class="_ _9"></span>C<span class="_ _20"> </span></span>+<span class="_ _1e"> </span><span class="ff8">C<span class="_ _28"></span>Y<span class="_ _36"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _28"></span>D<span class="_ _e"> </span></span>=<span class="_"> </span><span class="ff8">D<span class="_ _24"></span>C<span class="_ _20"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _27"></span>C<span class="_ _20"> </span></span>+<span class="_ _1e"> </span><span class="ff8">X<span class="_ _28"></span>D</span></div><div class="t m0 x110 h7 y274 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>2<span class="ff8">C<span class="_ _9"></span>X</span></div><div class="t m0 x110 h7 y275 ff8 fs3 fc0 sc0 ls0 ws0">Z<span class="_ _13"> </span><span class="ff6">y<span class="_ _e"> </span></span>Y<span class="_ _2f"> </span><span class="ff6">pun<span class="_ _12"></span>tos<span class="_ _e"> </span>de<span class="_ _e"> </span>tangencia<span class="_ _c"> </span>del<span class="_ _e"> </span>exc<span class="_ _10"></span>´<span class="_ _11"></span>ırculo</span></div><div class="t m0 x110 h7 y276 ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span><span class="ff8">A<span class="_ _c"> </span></span>con<span class="_ _c"> </span>lados</div><div class="t m0 xbf h7 y277 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _d"></span>−<span class="_ _a"></span>→</div><div class="t m0 xbf h7 y276 ff8 fs3 fc0 sc0 ls0 ws0">AB<span class="_ _f"> </span><span class="ff6">y</span></div><div class="t m0 xd9 h7 y277 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _3a"></span>→</div><div class="t m0 xd9 h9 y276 ff8 fs3 fc0 sc0 ls0 ws0">AC</div><div class="t m0 xa h7 y278 ff6 fs3 fc0 sc0 ls0 ws0">24,<span class="_ _c"> </span>25,<span class="_ _c"> </span>26<span class="_ _c"> </span>...<span class="_ _c"> </span>pueden<span class="_ _c"> </span>ser<span class="_ _c"> </span>sugerencias<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>amigos<span class="_ _c"> </span>de<span class="_ _f"> </span>la<span class="_ _e"> </span>matem´<span class="_ _a"></span>atica.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf11" class="pf w0 h0" data-page-no="11"><div class="pc pc11 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">14</div><div class="t m0 xb h5 yc1 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#5</div><div class="t m0 xa h7 y279 ff6 fs3 fc0 sc0 ls0 ws0">Comenzamos<span class="_"> </span>con<span class="_ _e"> </span>la<span class="_ _20"> </span>entrega<span class="_"> </span>de<span class="_ _e"> </span>notas<span class="_"> </span>relacionadas<span class="_ _e"> </span>con<span class="_ _e"> </span>la<span class="_"> </span>T<span class="_ _b"></span>eor<span class="_ _10"></span>´<span class="_ _11"></span>ıa<span class="_ _e"> </span>de<span class="_"> </span>N<span class="_ _24"></span>´<span class="_ _d"></span>umeros<span class="_ _e"> </span>(TN)<span class="_"> </span>y<span class="_ _e"> </span>el</div><div class="t m0 xb h7 y27a ff6 fs3 fc0 sc0 ls0 ws0">´<span class="_ _d"></span>alebra.<span class="_ _c"> </span>Aqu<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _c"> </span>v<span class="_ _3"></span>a<span class="_ _e"> </span>a<span class="_ _c"> </span>hab<span class="_ _24"></span>er<span class="_ _c"> </span>para<span class="_ _c"> </span>to<span class="_ _24"></span>dos<span class="_ _c"> </span>los<span class="_ _c"> </span>gustos,<span class="_ _c"> </span>desde<span class="_ _c"> </span>notas<span class="_ _e"> </span>trilladas<span class="_ _c"> </span>en<span class="_ _c"> </span>nuestra<span class="_ _e"> </span>ense<span class="_ _24"></span>˜<span class="_ _d"></span>nanza</div><div class="t m0 xb h7 y27b ff6 fs3 fc0 sc0 ls0 ws0">media<span class="_ _c"> </span>hasta<span class="_ _c"> </span>notas<span class="_ _c"> </span>necesarias<span class="_ _c"> </span>para<span class="_ _c"> </span>alumnos<span class="_ _c"> </span>de<span class="_ _c"> </span>alto<span class="_ _f"> </span>rendimien<span class="_ _3"></span>to.</div><div class="t m0 xa h7 y27c ff6 fs3 fc0 sc0 ls0 ws0">1<span class="_ _27"></span><span class="ffa">·<span class="_ _28"></span></span>-<span class="_ _f"> </span>Un<span class="_ _c"> </span>#<span class="_ _f"> </span>cualquiera<span class="_ _c"> </span>puede<span class="_ _f"> </span>expresarse<span class="_ _c"> </span>en<span class="_ _f"> </span>el<span class="_ _c"> </span>sistema<span class="_ _f"> </span>decimal<span class="_ _c"> </span>como<span class="_ _f"> </span>suma<span class="_ _c"> </span>de<span class="_ _f"> </span>potencias</div><div class="t m0 xb h7 y27d ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>base<span class="_ _c"> </span>10.<span class="_ _c"> </span>Por<span class="_ _e"> </span>ejemplo:<span class="_ _c"> </span><span class="ff8">abc<span class="_ _20"> </span></span>=<span class="_"> </span>100<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>10<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>,<span class="_ _c"> </span><span class="ff8">abcd<span class="_ _20"> </span></span>=<span class="_"> </span>1000<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>100<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>10<span class="ff8">c<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">d</span></div><div class="t m0 xa h7 y27e ff6 fs3 fc0 sc0 ls0 ws0">2<span class="ffa">·<span class="_ _3"></span><span class="ff6">-<span class="_"> </span>Un<span class="_"> </span>#<span class="_"> </span>lo<span class="_"> </span>llamamos<span class="_"> </span>Cuadrado<span class="_"> </span>P<span class="_ _3"></span>erfecto<span class="_"> </span>cuando<span class="_"> </span>su<span class="_"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ız<span class="_"> </span>cuadrada<span class="_"> </span>es<span class="_"> </span>un<span class="_"> </span>n<span class="_ _24"></span>´<span class="_ _d"></span>umero<span class="_"> </span>en<span class="_ _3"></span>tero</span></span></div><div class="t m0 xb h7 y27f ff6 fs3 fc0 sc0 ls0 ws0">(0<span class="ff8">,<span class="_ _1f"> </span></span>1<span class="ff8">,<span class="_ _1f"> </span></span>4<span class="ff8">,<span class="_ _1f"> </span></span>9<span class="ff8">,<span class="_ _1f"> </span></span>16<span class="ff8">,<span class="_ _1f"> </span>...,<span class="_ _1f"> </span>n</span></div><div class="t m0 x2d ha y280 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xaf h7 y27f ff6 fs3 fc0 sc0 ls0 ws0">).<span class="_ _c"> </span>V<span class="_ _b"></span>ea<span class="_ _c"> </span>que<span class="_ _f"> </span>la<span class="_ _e"> </span>diferencia<span class="_ _f"> </span>de<span class="_ _e"> </span>dos<span class="_ _f"> </span>(CP)<span class="_ _c"> </span>consecutiv<span class="_ _12"></span>os<span class="_ _c"> </span>es<span class="_ _c"> </span>igual<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _c"> </span>suma<span class="_ _c"> </span>de</div><div class="t m0 xb h7 y281 ff6 fs3 fc0 sc0 ls0 ws0">las<span class="_ _c"> </span>raices<span class="_ _c"> </span>cuadradas<span class="_ _c"> </span>de<span class="_ _c"> </span>ambos<span class="_ _c"> </span>#<span class="_ _c"> </span>ejemplo:<span class="_ _c"> </span>49<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>36<span class="_"> </span>=<span class="_"> </span>13<span class="_"> </span>=<span class="_"> </span>7<span class="_ _1e"> </span>+<span class="_ _1e"> </span>6</div><div class="t m0 xa h7 y282 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="_ _24"></span><span class="ffa">·<span class="_ _9"></span></span>-<span class="_ _e"> </span>M<span class="_ _24"></span>´<span class="_ _d"></span>ultiplos<span class="_"> </span>y<span class="_ _e"> </span>Divisores<span class="_ _e"> </span>de<span class="_ _e"> </span>un<span class="_ _e"> </span>#.<span class="_ _e"> </span>Ejemplo:<span class="_ _c"> </span>M<span class="_ _24"></span>´<span class="_ _d"></span>ultiplos<span class="_"> </span>de<span class="_ _e"> </span>6:<span class="_ _e"> </span>0<span class="ff8">,<span class="_ _1f"> </span></span>6<span class="ff8">,<span class="_ _1f"> </span></span>12<span class="ff8">,<span class="_ _1f"> </span></span>18<span class="ff8">,<span class="_ _1f"> </span>...<span class="_ _e"> </span></span>Divisores<span class="_ _e"> </span>de</div><div class="t m0 xb h7 y283 ff6 fs3 fc0 sc0 ls0 ws0">24:<span class="_ _c"> </span>1<span class="ff8">,<span class="_ _1f"> </span></span>2<span class="ff8">,<span class="_ _1f"> </span></span>3<span class="ff8">,<span class="_ _1f"> </span></span>4<span class="ff8">,<span class="_ _1f"> </span></span>6<span class="ff8">,<span class="_ _1f"> </span></span>8<span class="ff8">,<span class="_ _1f"> </span></span>24.</div><div class="t m0 xa h7 y284 ff6 fs3 fc0 sc0 ls0 ws0">4<span class="_ _1f"> </span><span class="ffa">·<span class="_ _33"></span></span>-<span class="_ _16"> </span>N´<span class="_ _d"></span>umeros<span class="_ _6"> </span>Primos:<span class="_ _6"> </span>Son<span class="_ _6"> </span>los<span class="_ _6"> </span>que<span class="_ _6"> </span>p<span class="_ _24"></span>oseen<span class="_ _6"> </span>2<span class="_ _6"> </span>divisores<span class="_ _6"> </span>(2<span class="ff8">,<span class="_ _1f"> </span></span>3<span class="ff8">,<span class="_ _1f"> </span></span>5<span class="ff8">,<span class="_ _1f"> </span></span>7<span class="ff8">,<span class="_ _1f"> </span></span>11<span class="ff8">,<span class="_ _1f"> </span></span>13<span class="ff8">,<span class="_ _1f"> </span>...</span>).<span class="_ _6"> </span>N<span class="_ _24"></span>´<span class="_ _d"></span>umeros</div><div class="t m0 xb h7 y285 ff6 fs3 fc0 sc0 ls0 ws0">Primos<span class="_ _20"> </span>entre<span class="_"> </span>s<span class="_ _10"></span>´<span class="_ _11"></span>ı:<span class="_ _e"> </span>Son<span class="_ _e"> </span>aquellos<span class="_ _e"> </span>que<span class="_ _e"> </span>solo<span class="_ _e"> </span>tienen<span class="_ _e"> </span>al<span class="_ _e"> </span>uno<span class="_ _20"> </span>como<span class="_ _e"> </span>divisor<span class="_ _e"> </span>com<span class="_ _24"></span>´<span class="_ _d"></span>un.<span class="_ _e"> </span>Ejemplo:<span class="_ _e"> </span>3<span class="_ _20"> </span>y<span class="_ _e"> </span>10,</div><div class="t m0 xb h7 y286 ff6 fs3 fc0 sc0 ls0 ws0">11<span class="_ _c"> </span>y<span class="_ _c"> </span>17,<span class="_ _c"> </span>4<span class="_ _c"> </span>y<span class="_ _c"> </span>9,<span class="_ _c"> </span>5,<span class="_ _c"> </span>8<span class="_ _f"> </span>y<span class="_ _e"> </span>21<span class="_ _c"> </span>...</div><div class="t m0 xa h7 y287 ff6 fs3 fc0 sc0 ls0 ws0">5<span class="_ _27"></span><span class="ffa">·<span class="_ _28"></span></span>-<span class="_ _f"> </span>M´<span class="_ _d"></span>aximo<span class="_ _f"> </span>Com´<span class="_ _d"></span>un<span class="_ _c"> </span>Divisor<span class="_ _f"> </span>(<span class="fff">mcd</span>):<span class="_ _c"> </span>De<span class="_ _f"> </span>todos<span class="_ _f"> </span>los<span class="_ _c"> </span>divisores<span class="_ _f"> </span>com<span class="_ _3"></span>unes<span class="_ _f"> </span>de<span class="_ _c"> </span>dos<span class="_ _c"> </span>o<span class="_ _f"> </span>v<span class="_ _b"></span>arios<span class="_ _f"> </span>#,</div><div class="t m0 xb h7 y288 ff6 fs3 fc0 sc0 ls0 ws0">el<span class="_ _c"> </span>ma<span class="_ _12"></span>y<span class="_ _3"></span>or<span class="_ _f"> </span>es<span class="_ _e"> </span>el<span class="_ _c"> </span><span class="fff">mcd</span>.<span class="_ _c"> </span>Ejemplo:<span class="_ _f"> </span><span class="fff">mcd</span>(24<span class="ff8">,<span class="_ _1f"> </span></span>32)<span class="_"> </span>=<span class="_"> </span>8.</div><div class="t m0 xa h7 y289 ff6 fs3 fc0 sc0 ls0 ws0">M<span class="_ _10"></span>´<span class="_ _11"></span>ınimo<span class="_ _c"> </span>Com<span class="_ _24"></span>´<span class="_ _d"></span>un<span class="_ _e"> </span>M<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>(<span class="fff">mcm</span>):<span class="_ _c"> </span>De<span class="_ _c"> </span>to<span class="_ _24"></span>dos<span class="_ _f"> </span>los<span class="_ _e"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplos<span class="_ _c"> </span>comunes<span class="_ _e"> </span>de<span class="_ _c"> </span>dos<span class="_ _f"> </span>o<span class="_ _e"> </span>v<span class="_ _3"></span>arios<span class="_ _c"> </span>#,<span class="_ _c"> </span>el</div><div class="t m0 xb h7 y28a ff6 fs3 fc0 sc0 ls0 ws0">menor<span class="_ _c"> </span>es<span class="_ _c"> </span>el<span class="_ _c"> </span><span class="fff">mcm</span>.<span class="_ _c"> </span>Ejemplo:<span class="_ _c"> </span><span class="fff">mcm</span>(8<span class="ff8">,<span class="_ _1f"> </span></span>10)<span class="_"> </span>=<span class="_"> </span>40</div><div class="t m0 xa h7 y28b ff6 fs3 fc0 sc0 ls0 ws0">¿C´<span class="_ _d"></span>omo<span class="_ _c"> </span>determinar<span class="_ _c"> </span>el<span class="_ _f"> </span>(<span class="fff">mcd</span>)<span class="_ _e"> </span>y<span class="_ _c"> </span>el<span class="_ _f"> </span>(<span class="fff">mcm</span>)<span class="_ _e"> </span>entre<span class="_ _e"> </span>v<span class="_ _3"></span>arios<span class="_ _c"> </span>n<span class="_ _24"></span>´<span class="_ _d"></span>umeros?</div><div class="t m0 xa h7 y28c ff6 fs3 fc0 sc0 ls0 ws0">Ejemplo:<span class="_ _c"> </span>Sean<span class="_ _c"> </span><span class="ff8">A<span class="_ _20"> </span></span>=<span class="_"> </span>30600,<span class="_ _c"> </span><span class="ff8">B<span class="_ _c"> </span></span>=<span class="_"> </span>4340,<span class="_ _c"> </span><span class="ff8">C<span class="_ _f"> </span></span>=<span class="_"> </span>2674200</div><div class="t m0 x81 h7 y28d ff6 fs3 fc0 sc0 ls0 ws0">o<span class="_ _c"> </span>sea<span class="_ _c"> </span><span class="ff8">A<span class="_ _20"> </span></span>=<span class="_"> </span>2</div><div class="t m0 x9d ha y28e ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x8e h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5</span></div><div class="t m0 x104 ha y28e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3c h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">7<span class="_ _1e"> </span></span>·<span class="_ _1e"> </span><span class="ff6">19,<span class="_ _c"> </span><span class="ff8">B<span class="_ _c"> </span></span>=<span class="_"> </span>2</span></div><div class="t m0 x3e ha y28e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf5 h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5<span class="_ _1e"> </span></span>·<span class="_ _1e"> </span><span class="ff6">7<span class="_ _1e"> </span></span>·<span class="_ _1e"> </span><span class="ff6">31,<span class="_ _c"> </span><span class="ff8">C<span class="_ _c"> </span></span>=<span class="_"> </span>2</span></div><div class="t m0 x112 ha y28e ff9 fs4 fc0 sc0 ls0 ws0">4</div><div class="t m0 xde h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5</span></div><div class="t m0 x113 ha y28e ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x114 h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">19</span></div><div class="t m0 x115 ha y28e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x116 h7 y28d ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">37</span></div><div class="t m0 xa h7 y28f ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _16"> </span><span class="fff">mcd<span class="ff6">(<span class="ff8">A,<span class="_ _1f"> </span>B<span class="_ _24"></span>,<span class="_ _1f"> </span>C<span class="_ _28"></span></span>)<span class="_ _16"> </span>=<span class="_ _16"> </span>2</span></span></span></div><div class="t m0 x117 ha y290 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x37 h7 y28f ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _e"> </span><span class="ff6">5<span class="_ _16"> </span>=<span class="_ _6"> </span>20<span class="_ _6"> </span>(V<span class="_ _b"></span>ea<span class="_ _6"> </span>que<span class="_ _36"> </span>se<span class="_ _6"> </span>toman<span class="_ _6"> </span>solo<span class="_ _36"> </span>las<span class="_ _6"> </span>bases<span class="_ _36"> </span>comunes<span class="_ _36"> </span>de<span class="_ _6"> </span>las</span></div><div class="t m0 xb h7 y291 ff6 fs3 fc0 sc0 ls0 ws0">p<span class="_ _24"></span>otencias<span class="_ _c"> </span>elev<span class="_ _3"></span>adas<span class="_ _c"> </span>al<span class="_ _c"> </span>menor<span class="_ _c"> </span>exp<span class="_ _24"></span>onente)</div><div class="t m0 x118 h7 y292 fff fs3 fc0 sc0 ls0 ws0">mcd<span class="ff6">(<span class="ff8">B<span class="_ _24"></span>,<span class="_ _33"> </span>C<span class="_ _9"></span></span>)<span class="_"> </span>=<span class="_"> </span>2</span></div><div class="t m0 x119 ha y293 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6b h7 y292 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5<span class="_"> </span>=<span class="_"> </span>20</span></div><div class="t m0 x118 h7 y294 fff fs3 fc0 sc0 ls0 ws0">mcd<span class="ff6">(<span class="ff8">A,<span class="_ _1f"> </span>C<span class="_ _9"></span></span>)<span class="_"> </span>=<span class="_"> </span>2</span></div><div class="t m0 xac ha y295 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x6b h7 y294 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5</span></div><div class="t m0 x8e ha y295 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x68 h7 y294 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">19<span class="_"> </span>=<span class="_"> </span>3800</span></div><div class="t m0 x118 h7 y296 fff fs3 fc0 sc0 ls0 ws0">mcm<span class="ff6">(<span class="ff8">A,<span class="_ _1f"> </span>B<span class="_ _9"></span>,<span class="_ _1f"> </span>C<span class="_ _9"></span></span>)<span class="_ _e"> </span>=<span class="_ _e"> </span>2</span></div><div class="t m0 x36 ha y297 ff9 fs4 fc0 sc0 ls0 ws0">4</div><div class="t m0 xf h7 y296 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5</span></div><div class="t m0 xf9 ha y297 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xb5 h7 y296 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">7<span class="_ _1e"> </span></span>·<span class="_ _21"> </span><span class="ff6">19</span></div><div class="t m0 xdc ha y297 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xcf h7 y296 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">31<span class="_ _1e"> </span></span>·<span class="_ _21"> </span><span class="ff6">37<span class="_ _f"> </span>(V<span class="_ _10"></span>ean<span class="_ _f"> </span>que<span class="_ _c"> </span>se<span class="_ _f"> </span>toman<span class="_ _f"> </span>todas<span class="_ _f"> </span>las<span class="_ _c"> </span>bases<span class="_ _f"> </span>de<span class="_ _c"> </span>las</span></div><div class="t m0 xb h7 y298 ff6 fs3 fc0 sc0 ls0 ws0">p<span class="_ _24"></span>otencias<span class="_ _c"> </span>y<span class="_ _c"> </span>entre<span class="_ _e"> </span>las<span class="_ _c"> </span>comunes<span class="_ _e"> </span>la<span class="_ _c"> </span>de<span class="_ _c"> </span>may<span class="_ _3"></span>or<span class="_ _c"> </span>exp<span class="_ _24"></span>onente)</div><div class="t m0 x118 h7 y299 fff fs3 fc0 sc0 ls0 ws0">mcm<span class="ff6">(<span class="ff8">A,<span class="_ _1f"> </span>B<span class="_ _9"></span></span>)<span class="_"> </span>=<span class="_"> </span>2</span></div><div class="t m0 xac ha y29a ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x6b h7 y299 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">5</span></div><div class="t m0 x8e ha y29a ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x68 h7 y299 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span><span class="ff6">7<span class="_ _1e"> </span></span>·<span class="_ _1e"> </span><span class="ff6">19<span class="_ _1e"> </span></span>·<span class="_ _1e"> </span><span class="ff6">31</span></div><div class="t m0 xa h7 y29b ff6 fs3 fc0 sc0 ls0 ws0">6<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Reglas<span class="_ _c"> </span>de<span class="_ _c"> </span>divisibilidad:<span class="_ _c"> </span>Un<span class="_ _c"> </span>#<span class="_ _c"> </span>es<span class="_ _f"> </span>divisible<span class="_ _e"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>...</div><div class="t m0 xce h7 y29c ff6 fs3 fc0 sc0 ls0 ws0">2<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>su<span class="_ _f"> </span>´<span class="_ _d"></span>ultima<span class="_ _c"> </span>cifra<span class="_ _c"> </span>es<span class="_ _c"> </span>par<span class="_ _c"> </span>o<span class="_ _c"> </span>es<span class="_ _c"> </span>=<span class="_"> </span>0</div><div class="t m0 xce h7 y29d ff6 fs3 fc0 sc0 ls0 ws0">5<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>su<span class="_ _f"> </span>´<span class="_ _d"></span>ultima<span class="_ _c"> </span>cifra<span class="_ _c"> </span>es<span class="_ _c"> </span>0<span class="_ _c"> </span>o<span class="_ _c"> </span>5</div><div class="t m0 xd6 h7 y29e ff6 fs3 fc0 sc0 ls0 ws0">10<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>su<span class="_ _f"> </span>´<span class="_ _d"></span>ultima<span class="_ _c"> </span>cifra<span class="_ _c"> </span>es<span class="_ _c"> </span>=<span class="_"> </span>0</div><div class="t m0 xce h7 y29f ff6 fs3 fc0 sc0 ls0 ws0">3<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>al<span class="_ _c"> </span>sumar<span class="_ _c"> </span>to<span class="_ _24"></span>das<span class="_ _f"> </span>sus<span class="_ _e"> </span>cifras<span class="_ _c"> </span>se<span class="_ _c"> </span>obtiene<span class="_ _f"> </span>un<span class="_ _e"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>3</div><div class="t m0 xce h7 y2a0 ff6 fs3 fc0 sc0 ls0 ws0">9<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>al<span class="_ _c"> </span>sumar<span class="_ _c"> </span>to<span class="_ _24"></span>das<span class="_ _f"> </span>sus<span class="_ _e"> </span>cifras<span class="_ _c"> </span>se<span class="_ _c"> </span>obtiene<span class="_ _f"> </span>un<span class="_ _e"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>9</div><div class="t m0 xce h7 y49 ff6 fs3 fc0 sc0 ls0 ws0">4<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>las<span class="_ _c"> </span>dos<span class="_ _f"> </span>´<span class="_ _d"></span>ultimas<span class="_ _c"> </span>cifras<span class="_ _c"> </span>del<span class="_ _c"> </span>#<span class="_ _c"> </span>conforman<span class="_ _c"> </span>un<span class="_ _c"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>4</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf12" class="pf w0 h0" data-page-no="12"><div class="pc pc12 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">15</div><div class="t m0 xce h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">8<span class="ffa">−<span class="_ _16"> </span></span>si<span class="_ _e"> </span>las<span class="_ _c"> </span>tres<span class="_ _f"> </span>´<span class="_ _d"></span>ultimas<span class="_ _c"> </span>cifras<span class="_ _c"> </span>del<span class="_ _c"> </span>#<span class="_ _c"> </span>conforman<span class="_ _c"> </span>un<span class="_ _c"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>8</div><div class="t m0 xd6 h7 y2a1 ff6 fs3 fc0 sc0 ls0 ws0">11<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _f"> </span>al<span class="_ _f"> </span>restar<span class="_ _13"> </span>los<span class="_ _f"> </span>dos<span class="_ _f"> </span>resultados<span class="_ _13"> </span>de<span class="_ _f"> </span>sumar<span class="_ _13"> </span>las<span class="_ _f"> </span>cifras<span class="_ _f"> </span>de<span class="_ _13"> </span>orden<span class="_ _f"> </span>par<span class="_ _13"> </span>y<span class="_ _f"> </span>las<span class="_ _f"> </span>de</div><div class="t m0 x5f h7 y2a2 ff6 fs3 fc0 sc0 ls0 ws0">orden<span class="_ _c"> </span>impar,<span class="_ _c"> </span>se<span class="_ _c"> </span>obtiene<span class="_ _c"> </span>un<span class="_ _c"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>11,<span class="_ _c"> </span>veamos...</div><div class="t m0 x11a h9 y2a3 ff8 fs3 fc0 sc0 ls0 ws0">abcde<span class="_ _3b"> </span>S</div><div class="t m0 xac ha y2a4 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x6b h7 y2a3 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">d<span class="_ _3b"> </span>S</span></div><div class="t m0 xec ha y2a4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xad h7 y2a3 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">d<span class="_ _3b"> </span><span class="ffa">|</span>S</span></div><div class="t m0 x11b ha y2a4 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x6c h7 y2a3 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff8">S</span></div><div class="t m0 xef ha y2a4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd4 h7 y2a3 ffa fs3 fc0 sc0 ls0 ws0">|<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>11<span class="ff8">k</span></span></div><div class="t m0 xce h7 y2a5 ff6 fs3 fc0 sc0 ls0 ws0">6<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _e"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>2<span class="_ _e"> </span>y<span class="_ _c"> </span>3<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _e"> </span>misma<span class="_ _c"> </span>vez</div><div class="t m0 xd6 h7 y2a6 ff6 fs3 fc0 sc0 ls0 ws0">12<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _e"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>3<span class="_ _e"> </span>y<span class="_ _c"> </span>4<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _e"> </span>misma<span class="_ _c"> </span>vez</div><div class="t m0 xd6 h7 y2a7 ff6 fs3 fc0 sc0 ls0 ws0">15<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _e"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>3<span class="_ _e"> </span>y<span class="_ _c"> </span>5<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _e"> </span>misma<span class="_ _c"> </span>vez</div><div class="t m0 xd6 h7 y2a8 ff6 fs3 fc0 sc0 ls0 ws0">36<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _e"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>4<span class="_ _e"> </span>y<span class="_ _c"> </span>9<span class="_ _c"> </span>a<span class="_ _f"> </span>la<span class="_ _e"> </span>misma<span class="_ _c"> </span>vez</div><div class="t m0 x11a h7 y2a9 ff6 fs3 fc0 sc0 ls0 ws0">V<span class="_ _b"></span>ea<span class="_ _c"> </span>que<span class="_ _c"> </span>2<span class="_ _c"> </span>y<span class="_ _c"> </span>3,<span class="_ _c"> </span>3<span class="_ _c"> </span>y<span class="_ _c"> </span>4,<span class="_ _f"> </span>3<span class="_ _e"> </span>y<span class="_ _c"> </span>5,<span class="_ _c"> </span>4<span class="_ _f"> </span>y<span class="_ _e"> </span>9<span class="_ _c"> </span>son<span class="_ _f"> </span>#<span class="_ _e"> </span>primos<span class="_ _c"> </span>entre<span class="_ _e"> </span>s<span class="_ _10"></span>´<span class="_ _11"></span>ı</div><div class="t m0 x11a h7 y2aa ff6 fs3 fc0 sc0 ls0 ws0">Ejemplo:<span class="_ _c"> </span>1536<span class="_ _c"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or:<span class="_ _c"> </span>1<span class="ff8">,<span class="_ _1f"> </span></span>2<span class="ff8">,<span class="_ _1f"> </span></span>3<span class="ff8">,<span class="_ _1f"> </span></span>4<span class="ff8">,<span class="_ _1f"> </span></span>6<span class="ff8">,<span class="_ _1f"> </span></span>8<span class="ff8">,<span class="_ _1f"> </span></span>12<span class="ff8">,<span class="_ _1f"> </span>...,<span class="_ _1f"> </span></span>1536</div><div class="t m0 xd5 h7 y2ab ff6 fs3 fc0 sc0 ls0 ws0">no<span class="_ _c"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or:<span class="_ _c"> </span>5<span class="ff8">,<span class="_ _1f"> </span></span>10<span class="ff8">,<span class="_ _1f"> </span></span>9<span class="ff8">,<span class="_ _1f"> </span></span>11<span class="ff8">,<span class="_ _1f"> </span></span>36<span class="ff8">,<span class="_ _1f"> </span>...</span></div><div class="t m0 xce h7 y2ac ff6 fs3 fc0 sc0 ls0 ws0">7<span class="ffa">−<span class="_ _16"> </span></span>cuando<span class="_ _c"> </span>separamos<span class="_ _f"> </span>su<span class="_ _f"> </span>´<span class="_ _d"></span>ultima<span class="_ _c"> </span>cifra<span class="_ _f"> </span>y<span class="_ _f"> </span>m<span class="_ _3"></span>ultiplic´<span class="_ _a"></span>andola<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _f"> </span>2,<span class="_ _c"> </span>dicho<span class="_ _c"> </span>resultado<span class="_ _f"> </span>se</div><div class="t m0 x5f h7 y2ad ff6 fs3 fc0 sc0 ls0 ws0">le<span class="_ _13"> </span>resta<span class="_ _8"> </span>al<span class="_ _8"> </span>#<span class="_ _13"> </span>que<span class="_ _8"> </span>result´<span class="_ _d"></span>o<span class="_ _8"> </span>de<span class="_ _8"> </span>suprimir<span class="_ _13"> </span>la<span class="_ _36"> </span>´<span class="_ _d"></span>ultima<span class="_ _13"> </span>cifra<span class="_ _8"> </span>al<span class="_ _8"> </span>#<span class="_ _13"> </span>original,<span class="_ _8"> </span>obteniendo<span class="_ _13"> </span>un</div><div class="t m0 x5f h7 y2ae ff6 fs3 fc0 sc0 ls0 ws0">m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _e"> </span>de<span class="_ _c"> </span>7</div><div class="t m0 x11a h7 y2af ff6 fs3 fc0 sc0 ls0 ws0">Ejemplo:<span class="_"> </span>51492<span class="_ _e"> </span>:<span class="_ _e"> </span>2<span class="_ _29"> </span><span class="ffa">·<span class="_ _1f"></span></span>2<span class="_"> </span>=<span class="_"> </span>4,<span class="_"> </span>5149<span class="_ _1f"> </span><span class="ffa">−<span class="_ _29"></span></span>4<span class="_"> </span>=<span class="_"> </span>5145,<span class="_ _e"> </span>5<span class="_ _1f"> </span><span class="ffa">·<span class="_ _29"></span></span>2<span class="_"> </span>=<span class="_"> </span>10,<span class="_ _20"> </span>514<span class="_ _1f"> </span><span class="ffa">−<span class="_ _29"></span></span>10<span class="_"> </span>=<span class="_"> </span>504,<span class="_ _e"> </span>4<span class="_ _1f"> </span><span class="ffa">·<span class="_ _29"></span></span>2<span class="_"> </span>=<span class="_"> </span>8</div><div class="t m0 x11a h7 y2b0 ff6 fs3 fc0 sc0 ls0 ws0">50<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>8<span class="_"> </span>=<span class="_"> </span>42<span class="_ _c"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff6">51492<span class="_ _c"> </span>es<span class="_ _c"> </span>m<span class="_ _24"></span>´<span class="_ _d"></span>ultiplo<span class="_ _c"> </span>de<span class="_ _c"> </span>7</span></span></div><div class="t m0 xa h7 y2b1 ff6 fs3 fc0 sc0 ls0 ws0">Ahora<span class="_ _8"> </span>existe<span class="_ _8"> </span>una<span class="_ _8"> </span>regla<span class="_ _8"> </span>general<span class="_ _8"> </span>que<span class="_ _8"> </span>nos<span class="_ _8"> </span>p<span class="_ _24"></span>ermite<span class="_ _8"> </span>obtener<span class="_ _8"> </span>la<span class="_ _8"> </span>regla<span class="_ _8"> </span>de<span class="_ _8"> </span>divisibilidad<span class="_ _8"> </span>de</div><div class="t m0 xb h7 y2b2 ff6 fs3 fc0 sc0 ls0 ws0">cualquier<span class="_"> </span>#<span class="_ _1e"> </span>primo.<span class="_"> </span>En<span class="_"> </span>cualquier<span class="_ _21"> </span>caso<span class="_"> </span>debemos<span class="_"> </span>separar<span class="_ _21"> </span>la<span class="_"> </span>´<span class="_ _d"></span>ultima<span class="_"> </span>cifra<span class="_ _21"> </span>del<span class="_"> </span>#<span class="_ _21"> </span>y<span class="_"> </span>m<span class="_ _3"></span>ultiplicarlo</div><div class="t m0 xb h7 y2b3 ff6 fs3 fc0 sc0 ls0 ws0">p<span class="_ _24"></span>or<span class="_ _f"> </span>un<span class="_ _13"> </span>#n<span class="_ _13"> </span><span class="ff8">n<span class="_ _f"> </span></span>y<span class="_ _13"> </span>luego<span class="_ _f"> </span>realizar<span class="_ _13"> </span>el<span class="_ _13"> </span>mismo<span class="_ _f"> </span>algoritmo<span class="_ _13"> </span>que<span class="_ _13"> </span>la<span class="_ _f"> </span>regla<span class="_ _13"> </span>del<span class="_ _f"> </span>7.<span class="_ _13"> </span>El<span class="_ _13"> </span>problema<span class="_ _f"> </span>es<span class="_ _13"> </span>v<span class="_ _3"></span>er</div><div class="t m0 xb h7 y2b4 ff6 fs3 fc0 sc0 ls0 ws0">qui<span class="_ _3"></span>´<span class="_ _25"></span>en<span class="_ _c"> </span>es<span class="_ _c"> </span><span class="ff8">n</span>.</div><div class="t m0 xa h7 y2b5 ff6 fs3 fc0 sc0 ls0 ws0">Deb<span class="_ _24"></span>emos<span class="_ _c"> </span>buscar<span class="_ _c"> </span>qu´<span class="_ _a"></span>e<span class="_ _c"> </span>d<span class="_ _10"></span>´<span class="_ _11"></span>ıgitos<span class="_ _c"> </span>multiplicados<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>el<span class="_ _c"> </span>#<span class="_ _f"> </span>al<span class="_ _c"> </span>cual<span class="_ _c"> </span>le<span class="_ _f"> </span>estamos<span class="_ _e"> </span>inv<span class="_ _3"></span>estigando<span class="_ _f"> </span>la</div><div class="t m0 xb h7 y2b6 ff6 fs3 fc0 sc0 ls0 ws0">regla<span class="_ _13"> </span>de<span class="_ _13"> </span>divisibilidad<span class="_ _13"> </span>,<span class="_ _f"> </span>da<span class="_ _13"> </span>como<span class="_ _13"> </span>resultado<span class="_ _13"> </span>un<span class="_ _13"> </span>#<span class="_ _13"> </span>cuy<span class="_ _12"></span>a<span class="_ _8"> </span>´<span class="_ _d"></span>ultima<span class="_ _f"> </span>cifra<span class="_ _13"> </span>es<span class="_ _13"> </span>=<span class="_ _13"> </span>1.<span class="_ _f"> </span>Del<span class="_ _13"> </span>resultado</div><div class="t m0 xb h7 y2b7 ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _e"> </span>este<span class="_ _c"> </span>pro<span class="_ _24"></span>ducto<span class="_ _c"> </span>nos<span class="_ _c"> </span>in<span class="_ _3"></span>teresa<span class="_ _c"> </span>solo<span class="_ _c"> </span>las<span class="_ _c"> </span>cifras<span class="_ _e"> </span>que<span class="_ _c"> </span>queden<span class="_ _c"> </span>a<span class="_ _c"> </span>la<span class="_ _e"> </span>izquierda<span class="_ _c"> </span>del<span class="_ _c"> </span>1,<span class="_ _c"> </span>y<span class="_ _e"> </span>este<span class="_ _c"> </span>ser´<span class="_ _a"></span>a<span class="_ _e"> </span>el</div><div class="t m0 xb h7 y2b8 ff6 fs3 fc0 sc0 ls0 ws0">v<span class="_ _3"></span>alor<span class="_ _e"> </span>de<span class="_ _f"> </span><span class="ff8">n</span>.</div><div class="t m0 xa h7 y2b9 ff6 fs3 fc0 sc0 ls0 ws0">Ejemplo<span class="_ _c"> </span>Regla<span class="_ _c"> </span>del<span class="_ _c"> </span>97:<span class="_ _c"> </span>97<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>3<span class="_"> </span>=<span class="_"> </span>291<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>29</span></span></span></div><div class="t m0 x86 h7 y2ba ff6 fs3 fc0 sc0 ls0 ws0">Sea<span class="_ _c"> </span>12804:<span class="_ _c"> </span>4<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>29<span class="_"> </span>=<span class="_"> </span>116,<span class="_ _c"> </span>1280<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>116<span class="_"> </span>=<span class="_"> </span>1164,<span class="_ _c"> </span>4<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span></span>29<span class="_"> </span>=<span class="_"> </span>116,<span class="_ _c"> </span>116<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>116<span class="_"> </span>=<span class="_"> </span>0</div><div class="t m0 xa h7 y2bb ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff6">12804<span class="_ _c"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>97</span></span></div><div class="t m0 xcc h7 y2bc ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span>·<span class="_ _1e"> </span>−<span class="_ _1e"> </span>·<span class="_ _1e"> </span>−</div><div class="t m0 xb h7 y2bd ff6 fs3 fc0 sc0 ls0 ws0">7<span class="_ _9"></span><span class="ffa">·<span class="_ _28"></span></span>-<span class="_ _e"> </span>Divisibilidad:<span class="_ _c"> </span>El<span class="_ _e"> </span>n<span class="_ _24"></span>´<span class="_ _d"></span>umero<span class="_ _e"> </span>natural<span class="_ _c"> </span><span class="ff8">n<span class="_ _e"> </span></span>es<span class="_ _c"> </span>un<span class="_ _e"> </span>divisor<span class="_ _c"> </span>del<span class="_ _c"> </span>n<span class="_ _24"></span>´<span class="_ _d"></span>umero<span class="_ _e"> </span>natural<span class="_ _e"> </span><span class="ff8">m<span class="_ _c"> </span></span>si<span class="_ _e"> </span>existe<span class="_ _c"> </span><span class="ff8">x<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N</span></span></span></div><div class="t m0 xb h7 y2be ff6 fs3 fc0 sc0 ls0 ws0">tal<span class="_ _c"> </span>que<span class="_ _c"> </span><span class="ff8">m<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">nx<span class="_ _c"> </span></span>y<span class="_ _c"> </span>se<span class="_ _c"> </span>escrib<span class="_ _24"></span>e<span class="_ _c"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>m<span class="_ _c"> </span></span>o<span class="_ _c"> </span><span class="ff8">m</span></div><div class="t m0 x105 h7 y2bf ff6 fs3 fc0 sc0 ls0 ws0">.</div><div class="t m0 x105 h7 y2c0 ff6 fs3 fc0 sc0 ls0 ws0">.</div><div class="t m0 x105 h7 y2be ff6 fs3 fc0 sc0 ls0 ws0">.<span class="_ _c"> </span><span class="ff8">n</span>.<span class="_ _c"> </span>Se<span class="_ _c"> </span>lee<span class="_ _c"> </span><span class="ff8">n<span class="_ _c"> </span></span>divide<span class="_ _c"> </span>a<span class="_ _c"> </span><span class="ff8">m<span class="_ _f"> </span></span>o<span class="_ _e"> </span><span class="ff8">m<span class="_ _c"> </span></span>es<span class="_ _c"> </span>m<span class="_ _9"></span>´<span class="_ _d"></span>ultiplo<span class="_ _e"> </span>de<span class="_ _c"> </span><span class="ff8">n</span></div><div class="t m0 x41 h7 y2c1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>P<span class="_ _3"></span>ara<span class="_ _c"> </span>to<span class="_ _24"></span>do<span class="_ _c"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">Z</span></span></span></div><div class="t m0 x10 ha y2c2 ff9 fs4 fc0 sc0 ls0 ws0">+</div><div class="t m0 x38 h7 y2c1 ff6 fs3 fc0 sc0 ls0 ws0">;<span class="_ _c"> </span>1<span class="_"> </span><span class="ffa">|<span class="_ _20"> </span><span class="ff8">n<span class="_ _c"> </span></span></span>y<span class="_ _c"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>n</span></div><div class="t m0 x41 h7 y2c3 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>c<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">b<span class="_ _1e"> </span></span>±<span class="_ _1e"> </span><span class="ff8">c</span></span></div><div class="t m0 x41 h7 y2c4 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">bc<span class="_ _c"> </span><span class="ff6">;<span class="_ _c"> </span></span></span>∀<span class="ff8">c<span class="_ _20"> </span></span>∈<span class="_ _20"> </span><span class="ff10">Z</span></span></div><div class="t m0 x41 h7 y2c5 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>c<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">c</span></span></div><div class="t m0 x41 h7 y2c6 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>c<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff6">(<span class="ff8">bx<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">cy<span class="_ _24"></span></span>)<span class="_ _c"> </span></span>∀<span class="ff8">x,<span class="_ _1f"> </span>y<span class="_ _e"> </span></span>∈<span class="_ _20"> </span><span class="ff10">Z</span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf13" class="pf w0 h0" data-page-no="13"><div class="pc pc13 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">16</div><div class="t m0 x41 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>a<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span></span>±<span class="ff8">b</span></span></div><div class="t m0 x41 h7 y2a1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b</span>,<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span>><span class="_ _20"> </span></span>0<span class="_ _c"> </span>,<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span>><span class="_ _20"> </span></span>0<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">b<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 x41 h7 y2c7 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Dado<span class="_ _13"> </span>un<span class="_ _8"> </span>p<span class="_ _24"></span>olinomio<span class="_ _8"> </span><span class="ff8">P<span class="_ _2"> </span></span>=<span class="_ _8"> </span><span class="ff8">p</span></div><div class="t m0 x105 he y2c8 ffd fs4 fc0 sc0 ls0 ws0">α</div><div class="t m0 xcc h11 y2c9 ff11 fs7 fc0 sc0 ls0 ws0">1</div><div class="t m0 x63 h7 y2c7 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _20"> </span><span class="ff8">p</span></div><div class="t m0 xb6 he y2c8 ffd fs4 fc0 sc0 ls0 ws0">α</div><div class="t m0 x55 h11 y2c9 ff11 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf1 h7 y2c7 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _20"> </span><span class="ff8">p</span></div><div class="t m0 x110 he y2c8 ffd fs4 fc0 sc0 ls0 ws0">α</div><div class="t m0 x3f h11 y2c9 ff11 fs7 fc0 sc0 ls0 ws0">3</div><div class="t m0 xc0 h7 y2c7 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _20"> </span>·<span class="_ _20"> </span>·<span class="_ _20"> </span>·<span class="ff8">p</span></div><div class="t m0 x11c he y2c8 ffd fs4 fc0 sc0 ls0 ws0">α</div><div class="t m0 xf6 h12 y2ca ff12 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1e h7 y2c7 ff6 fs3 fc0 sc0 ls0 ws0">decimos<span class="_ _8"> </span>que<span class="_ _8"> </span>la<span class="_ _8"> </span>can<span class="_ _12"></span>tidad<span class="_ _8"> </span>de</div><div class="t m0 x5f h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">divisores<span class="_ _c"> </span><span class="ff8">D<span class="_ _f"> </span></span>de<span class="_ _c"> </span><span class="ff8">P<span class="_ _36"> </span></span>es<span class="_ _f"> </span><span class="ff8">D<span class="_ _20"> </span></span>=<span class="_"> </span>(<span class="ff8">α</span></div><div class="t m0 xb9 ha y2cc ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x11d h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>1)(<span class="ff8">α</span></div><div class="t m0 x11e ha y2cc ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x11f h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>1)(<span class="ff8">α</span></div><div class="t m0 x6d ha y2cc ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x66 h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>1)<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span>·<span class="_ _1e"> </span>·<span class="_ _1e"> </span>·</span>(<span class="ff8">α</span></div><div class="t m0 x120 he y2cc ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xdb h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>1)</div><div class="t m0 x41 h7 y2cd ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Sea<span class="_ _e"> </span><span class="ff8">p<span class="_ _c"> </span></span>primo<span class="_ _c"> </span>tal<span class="_ _f"> </span>que<span class="_ _e"> </span><span class="ff8">p<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>ab<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">p<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">a<span class="_ _c"> </span><span class="ff6">o<span class="_ _c"> </span></span>p<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">b</span></span></div><div class="t m0 x41 h7 y2ce ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>T<span class="_ _10"></span>o<span class="_ _24"></span>do<span class="_"> </span>#<span class="_"> </span>primo<span class="_"> </span>may<span class="_ _3"></span>or<span class="_"> </span>que<span class="_"> </span>3<span class="_"> </span>puede<span class="_"> </span>expresarse<span class="_"> </span>como<span class="_"> </span>4<span class="ff8">n<span class="_ _27"></span><span class="ffa">±<span class="_ _27"></span></span></span>1;<span class="_"> </span>6<span class="ff8">k<span class="_ _29"> </span><span class="ffa">±<span class="_ _27"></span></span></span>1<span class="_"> </span>con<span class="_"> </span><span class="ff8">n,<span class="_ _1f"> </span>k<span class="_ _e"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N</span></span></span></div><div class="t m0 x121 h8 y2cf ff7 fs4 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xa h7 y2d0 ff6 fs3 fc0 sc0 ls0 ws0">8<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span><span class="fff">mcd<span class="_ _c"> </span></span>y<span class="_ _f"> </span><span class="fff">mcm</span>.<span class="_ _e"> </span>Conv<span class="_ _3"></span>eniemos<span class="_ _c"> </span>que<span class="_ _c"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)<span class="_"> </span>=<span class="_"> </span><span class="fff">mcd</span>(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)<span class="_ _c"> </span>y<span class="_ _c"> </span>[<span class="ff8">a,<span class="_ _1f"> </span>b</span>]<span class="_"> </span>=<span class="_"> </span><span class="fff">mcm</span>(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)</div><div class="t m0 x41 h7 y2d1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">|<span class="_ _20"> </span></span>c<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff6">(<span class="ff8">b,<span class="_ _1f"> </span>c</span>)</span></span></div><div class="t m0 x41 h7 y2d2 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">ma,<span class="_ _29"> </span>mb</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">m</span>(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)<span class="_ _f"> </span><span class="ffa">∀<span class="ff8">m<span class="_ _21"> </span></span>∈<span class="_ _20"> </span><span class="ff10">Z</span></span></div><div class="t m0 x105 ha y2d3 ff9 fs4 fc0 sc0 ls0 ws0">+</div><div class="t m0 xdd h7 y2d2 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">a,<span class="_ _1f"> </span>b<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N</span></span></span></div><div class="t m0 x41 h7 y2d4 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a,<span class="_ _29"> </span>b</span>)<span class="_"> </span>=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span><span class="ffa">±<span class="_ _1e"> </span></span>b,<span class="_ _1f"> </span>a</span>)<span class="_"> </span>=<span class="_"> </span>(<span class="ff8">b,<span class="_ _1f"> </span>b<span class="_ _1e"> </span><span class="ffa">±<span class="_ _1e"> </span></span>a</span>)</div><div class="t m0 x41 h7 y2d5 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span>(<span class="ff8">m,<span class="_ _1f"> </span>n</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">d<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">m<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>ad,<span class="_ _1f"> </span>n<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>bd<span class="ff6">;<span class="_ _c"> </span></span>a,<span class="_ _1f"> </span>b<span class="_ _20"> </span></span>∈<span class="_ _20"> </span><span class="ff10">Z<span class="ff6">,<span class="_ _c"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)<span class="_"> </span>=<span class="_"> </span>1</span></span></span></div><div class="t m0 x41 h7 y2d6 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a,<span class="_ _29"> </span>b</span>)<span class="_"> </span>=</div><div class="t m0 x46 h9 y2d7 ff8 fs3 fc0 sc0 ls0 ws0">ab</div><div class="t m0 xa6 h7 y2d8 ff6 fs3 fc0 sc0 ls0 ws0">[<span class="ff8">a,<span class="_ _1f"> </span>b</span>]</div><div class="t m0 x36 h7 y2d6 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span>[<span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c</span>]<span class="_"> </span>=</div><div class="t m0 xcf h7 y2d7 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c</span>)<span class="_ _1e"> </span><span class="ffa">·<span class="_ _1e"> </span><span class="ff8">abc</span></span></div><div class="t m0 xdc h7 y2d8 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a,<span class="_ _1f"> </span>b</span>)(<span class="ff8">b,<span class="_ _1f"> </span>c</span>)(<span class="ff8">c,<span class="_ _1f"> </span>a</span>)</div><div class="t m0 xa h7 y2d9 ff6 fs3 fc0 sc0 ls0 ws0">9<span class="_ _27"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _13"> </span>Congruencia:<span class="_ _f"> </span>Sean<span class="_ _f"> </span><span class="ff8">a,<span class="_ _1f"> </span>b<span class="_ _c"> </span><span class="ffa">∈<span class="_ _f"> </span><span class="ff10">Z</span></span></span>,<span class="_ _f"> </span><span class="ff8">m<span class="_ _c"> </span><span class="ffa">∈<span class="_ _f"> </span><span class="ff10">N</span></span></span></div><div class="t m0 x11f h8 y2da ff7 fs4 fc0 sc0 ls0 ws0">∗</div><div class="t m0 x54 h7 y2d9 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _f"> </span><span class="ff6">“<span class="ff8">a</span>”<span class="_ _f"> </span>es<span class="_ _13"> </span>congruen<span class="_ _3"></span>te<span class="_ _f"> </span>con<span class="_ _13"> </span>“<span class="ff8">b</span>”<span class="_ _f"> </span>m´<span class="_ _d"></span>odulo<span class="_ _13"> </span>“<span class="ff8">m</span>”</span></span></div><div class="t m0 xb h7 y2db ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b<span class="_ _e"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _f"> </span><span class="ff8">m</span>))<span class="_ _e"> </span>si<span class="_ _c"> </span><span class="ff8">a<span class="_ _c"> </span></span>y<span class="_ _f"> </span><span class="ff8">b<span class="_ _e"> </span></span>dejan<span class="_ _c"> </span>el<span class="_ _c"> </span>mismo<span class="_ _f"> </span>resto<span class="_ _e"> </span>al<span class="_ _c"> </span>dividirlos<span class="_ _f"> </span>por<span class="_ _c"> </span>“<span class="ff8">m</span>”</div><div class="t m0 x41 h7 y2dc ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">a<span class="_ _21"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)<span class="_"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">b<span class="_ _c"> </span><span class="ff6">es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span></span>m</span></span></div><div class="t m0 x41 h7 y2dd ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c,<span class="_ _1f"> </span>d,<span class="_ _1f"> </span>k<span class="_ _e"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N</span></span></span></div><div class="t m0 x104 h8 y2de ff7 fs4 fc0 sc0 ls0 ws0">∗</div><div class="t m0 x51 h7 y2dd ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N<span class="_ _e"> </span></span></span></span>y<span class="_ _f"> </span><span class="ff8">a<span class="_ _21"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b</span>,<span class="_ _c"> </span><span class="ff8">c<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>d<span class="_ _c"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)<span class="_"> </span>=<span class="_ _4"></span><span class="ffa">⇒</span></div><div class="t m0 x4e h7 y2df ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _16"> </span><span class="ff8">a<span class="_ _33"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>d<span class="ff6">,<span class="_ _c"> </span></span>a<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">c<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">b<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">d<span class="ff6">,<span class="_ _c"> </span></span>ac<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">bd<span class="ff6">,<span class="_ _c"> </span></span>k<span class="_ _24"></span>a<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">k<span class="_ _24"></span>b<span class="_ _c"> </span><span class="ff6">(mo<span class="_ _24"></span>d<span class="_ _c"> </span></span>m<span class="ff6">)</span></span></div><div class="t m0 x4e h7 y2e0 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _16"> </span><span class="ff8">a</span></div><div class="t m0 x80 he y2e1 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8b h7 y2e0 ffa fs3 fc0 sc0 ls0 ws0">≡<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x3 he y2e1 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x122 h7 y2e0 ff6 fs3 fc0 sc0 ls0 ws0">(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)</div><div class="t m0 x4e h7 y2e2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _16"> </span><span class="ff8">a<span class="_ _21"> </span><span class="ff6">:<span class="_"> </span></span>k<span class="_ _e"> </span></span>≡<span class="_ _20"> </span><span class="ff8">b<span class="_ _20"> </span><span class="ff6">:<span class="_"> </span></span>k<span class="_ _f"> </span><span class="ff6">(mo<span class="_ _24"></span>d<span class="_ _c"> </span></span>m<span class="ff6">)<span class="_ _c"> </span>si<span class="_ _c"> </span>(</span>k<span class="_ _9"></span>,<span class="_ _1f"> </span>m<span class="ff6">)<span class="_"> </span>=<span class="_"> </span>1<span class="_ _c"> </span>y<span class="_ _c"> </span></span>a<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>k<span class="_ _24"></span>c<span class="_ _c"> </span><span class="ff6">y<span class="_ _c"> </span></span>b<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>k<span class="_ _24"></span>d</span></div><div class="t m0 x41 h7 y2e3 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">a<span class="_ _21"> </span><span class="ffa">≡<span class="_ _20"> </span></span>a<span class="_ _c"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)</div><div class="t m0 x41 h7 y2e4 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">a<span class="_ _c"> </span><span class="ff6">(mo<span class="_ _24"></span>d<span class="_ _c"> </span></span>m<span class="ff6">)</span></span></span></div><div class="t m0 x41 h7 y2e5 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">b<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>c<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">c<span class="_ _c"> </span><span class="ff6">(mo<span class="_ _24"></span>d<span class="_ _c"> </span></span>m<span class="ff6">)</span></span></span></div><div class="t m0 x41 h7 y2e6 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>b<span class="_ _c"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff6">(<span class="ff8">a,<span class="_ _1f"> </span>m</span>)<span class="_"> </span></span>≡<span class="_ _20"> </span><span class="ff6">(<span class="ff8">b,<span class="_ _1f"> </span>m</span>)<span class="_ _c"> </span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)</span></span></div><div class="t m0 x41 h7 y2e7 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">ax<span class="_ _20"> </span><span class="ffa">≡<span class="_ _20"> </span></span>ay<span class="_ _f"> </span></span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">m</span>)<span class="_ _c"> </span>y<span class="_ _c"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>m</span>)<span class="_"> </span>=<span class="_"> </span>1<span class="_"> </span>=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>≡<span class="_ _20"> </span><span class="ff8">y<span class="_ _f"> </span><span class="ff6">(mod<span class="_ _f"> </span></span>m<span class="ff6">)</span></span></span></div><div class="t m0 xa h7 y2e8 ff6 fs3 fc0 sc0 ls0 ws0">9<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>T<span class="_ _b"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>F<span class="_ _b"></span>ermat:<span class="_ _c"> </span>Sea<span class="_ _c"> </span><span class="ff8">p<span class="_ _c"> </span></span>primo<span class="_ _f"> </span>y<span class="_ _e"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N<span class="_ _20"> </span></span></span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">n</span></span></div><div class="t m0 x123 he y2e9 ffd fs4 fc0 sc0 ls0 ws0">p</div><div class="t m0 x26 h7 y2e8 ffa fs3 fc0 sc0 ls0 ws0">≡<span class="_ _20"> </span><span class="ff8">n<span class="_ _c"> </span><span class="ff6">(mo<span class="_ _24"></span>d<span class="_ _c"> </span></span>p<span class="ff6">)</span></span></div><div class="t m0 x40 h7 y2ea ff6 fs3 fc0 sc0 ls0 ws0">P<span class="_ _3"></span>eque<span class="_ _24"></span>˜<span class="_ _d"></span>no<span class="_ _c"> </span>teorema<span class="_ _c"> </span>de<span class="_ _c"> </span>F<span class="_ _b"></span>ermat:</div><div class="t m0 xc6 h7 y2eb ff6 fs3 fc0 sc0 ls0 ws0">Sea<span class="_ _c"> </span><span class="ff8">p<span class="_ _c"> </span></span>primo,<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">Z</span></span></span></div><div class="t m0 x103 ha y2ec ff9 fs4 fc0 sc0 ls0 ws0">+</div><div class="t m0 x124 h7 y2eb ff6 fs3 fc0 sc0 ls0 ws0">;<span class="_ _c"> </span><span class="ff8">p<span class="_ _20"> </span><span class="ff10">-<span class="_ _20"> </span></span>a<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 x63 ha y2ed ffd fs4 fc0 sc0 ls0 ws0">p<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x125 h7 y2eb ffa fs3 fc0 sc0 ls0 ws0">≡<span class="_ _20"> </span><span class="ff6">1<span class="_ _c"> </span>(mo<span class="_ _24"></span>d<span class="_ _c"> </span><span class="ff8">p</span>)</span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf14" class="pf w0 h0" data-page-no="14"><div class="pc pc14 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">17</div><div class="t m0 x40 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">T<span class="_ _b"></span>eorema<span class="_ _8"> </span>de<span class="_ _36"> </span>Euler:<span class="_ _36"> </span>Sean<span class="_ _36"> </span><span class="ff8">a,<span class="_ _1f"> </span>m<span class="_ _6"> </span><span class="ffa">∈<span class="_ _36"> </span><span class="ff10">N</span></span></span>;<span class="_ _36"> </span>(<span class="ff8">a,<span class="_ _1f"> </span>m</span>)<span class="_ _6"> </span>=<span class="_ _6"> </span>1<span class="_ _36"> </span>=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _36"> </span><span class="ff8">a</span></span></div><div class="t m0 x126 ha y80 ffd fs4 fc0 sc0 ls0 ws0">φ<span class="ff9">(</span>m<span class="ff9">)</span></div><div class="t m0 x127 h7 y9 ffa fs3 fc0 sc0 ls0 ws0">≡<span class="_ _36"> </span><span class="ff6">1<span class="_ _36"> </span>(mo<span class="_ _24"></span>d<span class="_ _36"> </span><span class="ff8">m</span>)<span class="_ _36"> </span>donde</span></div><div class="t m0 xb h7 y81 ff8 fs3 fc0 sc0 ls0 ws0">φ<span class="ff6">(</span>m<span class="ff6">)<span class="_ _c"> </span>es<span class="_ _f"> </span>el<span class="_ _c"> </span>indicador<span class="_ _f"> </span>y<span class="_ _c"> </span>nos<span class="_ _c"> </span>da<span class="_ _f"> </span>la<span class="_ _c"> </span>cantidad<span class="_ _c"> </span>de<span class="_ _c"> </span>#<span class="_ _f"> </span>primos<span class="_ _c"> </span>con<span class="_ _f"> </span></span>m<span class="ff6">,<span class="_ _c"> </span>no<span class="_ _f"> </span>ma<span class="_ _3"></span>yores<span class="_ _e"> </span>que<span class="_ _c"> </span>´<span class="_ _a"></span>el<span class="_ _f"> </span>tal<span class="_ _c"> </span>que</span></div><div class="t m0 xb h7 y2ee ff8 fs3 fc0 sc0 ls0 ws0">φ<span class="ff6">(</span>p<span class="ff6">)<span class="_"> </span>=<span class="_"> </span></span>p<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span><span class="ff6">1<span class="_ _c"> </span>siendo<span class="_ _c"> </span></span></span>p<span class="_ _c"> </span><span class="ff6">primo.</span></div><div class="t m0 xa h7 y2ef ff6 fs3 fc0 sc0 ls0 ws0">11,<span class="_ _c"> </span>12,<span class="_ _c"> </span>13,<span class="_ _c"> </span>...,<span class="_ _c"> </span>pueden<span class="_ _c"> </span>ser<span class="_ _c"> </span>sugerencias<span class="_ _c"> </span>de<span class="_ _f"> </span>los<span class="_ _e"> </span>amigos<span class="_ _c"> </span>lectores.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">18</div><div class="t m0 xb h5 yc1 ff1 fs2 fc0 sc0 ls0 ws0">Lecci´<span class="_ _7"></span>on<span class="_ _6"> </span>#6</div><div class="t m0 xa h7 yc2 ff6 fs3 fc0 sc0 ls0 ws0">El<span class="_ _13"> </span>´<span class="_ _d"></span>algebra<span class="_ _13"> </span>es<span class="_ _13"> </span>una<span class="_ _f"> </span>de<span class="_ _13"> </span>las<span class="_ _13"> </span>disciplinas<span class="_ _13"> </span>insigneas<span class="_ _f"> </span>dentro<span class="_ _f"> </span>del<span class="_ _13"> </span>estudio<span class="_ _13"> </span>de<span class="_ _13"> </span>las<span class="_ _f"> </span>matem´<span class="_ _a"></span>aticas.</div><div class="t m0 xb h7 yc3 ff6 fs3 fc0 sc0 ls0 ws0">En<span class="_ _c"> </span>estas<span class="_ _f"> </span>notas<span class="_ _c"> </span>tenemos<span class="_ _c"> </span>en<span class="_ _f"> </span>cuen<span class="_ _3"></span>ta<span class="_ _f"> </span>el<span class="_ _c"> </span>traba<span class="_ _9"></span>jo<span class="_ _f"> </span>con<span class="_ _c"> </span>p<span class="_ _24"></span>olinomios,<span class="_ _f"> </span>ecuaciones,<span class="_ _c"> </span>desigualdades<span class="_ _f"> </span>y</div><div class="t m0 xb h7 yc4 ff6 fs3 fc0 sc0 ls0 ws0">funciones<span class="_ _c"> </span>en<span class="_ _12"></span>tre<span class="_ _c"> </span>tan<span class="_ _12"></span>tas<span class="_ _c"> </span>l<span class="_ _10"></span>´<span class="_ _11"></span>ıneas<span class="_ _c"> </span>que<span class="_ _c"> </span>contempla<span class="_ _e"> </span>este<span class="_ _c"> </span>tema.</div><div class="t m0 xa h7 y151 ff6 fs3 fc0 sc0 ls0 ws0">1<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Pro<span class="_ _24"></span>ductos<span class="_ _c"> </span>Notables:</div><div class="t m0 x7c h7 y2f0 ff6 fs3 fc0 sc0 ls0 ws0">A<span class="_ _c"> </span>los<span class="_ _c"> </span>m´<span class="_ _d"></span>as<span class="_ _f"> </span>conocidos<span class="_ _c"> </span>incorp<span class="_ _24"></span>oramos<span class="_ _f"> </span>estos<span class="_ _e"> </span>de<span class="_ _c"> </span>gran<span class="_ _c"> </span>aplicaci´<span class="_ _a"></span>on</div><div class="t m0 x21 h7 y2f1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a<span class="_ _33"> </span><span class="ffa">±<span class="_ _1e"> </span></span>b</span>)</div><div class="t m0 xc5 ha y2f2 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x32 h7 y2f1 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x34 ha y2f2 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x6a h7 y2f1 ffa fs3 fc0 sc0 ls0 ws0">±<span class="_ _1e"> </span><span class="ff6">3<span class="ff8">a</span></span></div><div class="t m0 xf ha y2f2 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10 h7 y2f1 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span>3</span>ab</div><div class="t m0 x11d h8 y2f2 ff7 fs4 fc0 sc0 ls0 ws0">±</div><div class="t m0 x4a h9 y2f1 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x6 ha y2f2 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x21 h7 y2f3 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a<span class="_ _33"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)</div><div class="t m0 x128 ha y2f4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xab h7 y2f3 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x9d ha y2f4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x13 h7 y2f3 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 xf9 ha y2f4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb5 h7 y2f3 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 x82 ha y2f4 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa0 h7 y2f3 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>2<span class="ff8">ab<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>2<span class="ff8">bc<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>2<span class="ff8">ca</span></div><div class="t m0 x21 h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a<span class="_ _33"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)</div><div class="t m0 x128 ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xab h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x9d ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x13 h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 xf9 ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xb5 h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 x82 ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xa0 h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>3<span class="ff8">a</span></div><div class="t m0 xcc ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7 h7 y2f5 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span>3</span>a</div><div class="t m0 x129 ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12a h7 y2f5 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span>3</span>ab</div><div class="t m0 xbb ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6c h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>3<span class="ff8">b</span></div><div class="t m0 x16 ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x17 h7 y2f5 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span>3</span>ac</div><div class="t m0 x12b ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xc2 h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>3<span class="ff8">bc</span></div><div class="t m0 x12c ha y2f6 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12d h7 y2f5 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>6<span class="ff8">abc</span></div><div class="t m0 x21 h7 y2f7 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>(<span class="ff8">a<span class="_ _33"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)(<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)(<span class="ff8">c<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x12e ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x82 h7 y2f7 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>a</div><div class="t m0 x105 ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x62 h7 y2f7 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ab</div><div class="t m0 xe4 ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x99 h7 y2f7 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x5d ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xfb h7 y2f7 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ac</div><div class="t m0 xaa ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12f h7 y2f7 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">bc</span></div><div class="t m0 xe0 ha y2f8 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xbf h7 y2f7 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>2<span class="ff8">abc</span></div><div class="t m0 xa h7 y2f9 ff6 fs3 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ffa">·<span class="ff6">-<span class="_"> </span>F<span class="_ _10"></span>actorizaci´<span class="_ _a"></span>on:<span class="_"> </span>Al<span class="_ _21"> </span>factor<span class="_"> </span>com<span class="_ _24"></span>´<span class="_ _d"></span>un,<span class="_"> </span>diferencia<span class="_ _21"> </span>de<span class="_"> </span>cuadrados<span class="_"> </span>y<span class="_"> </span>trinomio<span class="_"> </span>agregamos<span class="_"> </span>otras</span></span></div><div class="t m0 xb h7 y2fa ff6 fs3 fc0 sc0 ls0 ws0">formas...</div><div class="t m0 x21 h7 y2fb ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>F<span class="_ _10"></span>actor<span class="_ _c"> </span>com<span class="_ _24"></span>´<span class="_ _d"></span>un<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>agrupamiento,<span class="_ _e"> </span>ejemplo:</div><div class="t m0 x7c h7 y2fc ff8 fs3 fc0 sc0 ls0 ws0">ab<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ac<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>mb<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>mc<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>a<span class="ff6">(</span>b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c<span class="ff6">)<span class="_ _1e"> </span>+<span class="_ _1e"> </span></span>m<span class="ff6">(</span>b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c<span class="ff6">)<span class="_"> </span>=<span class="_"> </span>(</span>b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c<span class="ff6">)(</span>a<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b<span class="ff6">)</span></div><div class="t m0 x21 h7 y2fd ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Suma<span class="_ _e"> </span>y<span class="_ _c"> </span>Diferencia<span class="_ _c"> </span>de<span class="_ _f"> </span>Cubos</div><div class="t m0 x7c h9 y2fe ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 xb0 ha y2ff ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x42 h7 y2fe ffa fs3 fc0 sc0 ls0 ws0">±<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x85 ha y2ff ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xa5 h7 y2fe ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span><span class="ffa">±<span class="_ _1e"> </span></span>b</span>)(<span class="ff8">a</span></div><div class="t m0 x68 ha y2ff ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf9 h7 y2fe ffa fs3 fc0 sc0 ls0 ws0">∓<span class="_ _1e"> </span><span class="ff8">ab<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b</span></div><div class="t m0 x130 ha y2ff ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xad h7 y2fe ff6 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 x21 h7 y300 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Otras<span class="_ _e"> </span>sumas</div><div class="t m0 x7c h7 y301 ff6 fs3 fc0 sc0 ls0 ws0">ejemplo<span class="_ _c"> </span>1)<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x46 ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6a h7 y301 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>a</div><div class="t m0 xf4 ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x37 h7 y301 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ab</div><div class="t m0 x82 ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa0 h7 y301 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x131 ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x62 h7 y301 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ac</div><div class="t m0 x125 ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x129 h7 y301 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">bc</span></div><div class="t m0 xfb ha y302 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x132 h7 y301 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>2<span class="ff8">abc</span></div><div class="t m0 x7c h7 y303 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x8f ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4d h7 y303 ff8 fs3 fc0 sc0 ls0 ws0">b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ab</div><div class="t m0 x128 ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x133 h7 y303 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x4 ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3b h7 y303 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>abc<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>abc<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b</div><div class="t m0 x134 ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x98 h7 y303 ff8 fs3 fc0 sc0 ls0 ws0">c<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>ac</div><div class="t m0 xb8 ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3f h7 y303 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">bc</span></div><div class="t m0 x10d ha y304 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7c h7 y305 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">ab</span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)<span class="_ _1e"> </span>+<span class="_ _1e"> </span><span class="ff8">ac</span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)<span class="_ _1e"> </span>+<span class="_ _1e"> </span><span class="ff8">bc</span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)<span class="_ _1e"> </span>+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 xa1 ha y306 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x56 h7 y305 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)</div><div class="t m0 x7c h7 y307 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)(<span class="ff8">ab<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">ac<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">bc<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 x52 ha y308 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa0 h7 y307 ff6 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 x7c h7 y309 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)[<span class="ff8">a</span>(<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)<span class="_ _1e"> </span>+<span class="_ _1e"> </span><span class="ff8">c</span>(<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)]</div><div class="t m0 x7c h7 y30a ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span>)(<span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)</div><div class="t m0 x7c h7 y30b ff6 fs3 fc0 sc0 ls0 ws0">ejemplo<span class="_ _c"> </span>2)<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x46 ha y30c ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x119 h7 y30b ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x8d ha y30c ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xae h7 y30b ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 xb5 ha y30c ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x7e h7 y30b ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff6">3<span class="ff8">abc</span></span></div><div class="t m0 x7c h7 y30d ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c</span>)(<span class="ff8">a</span></div><div class="t m0 x47 ha y30e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3b h7 y30d ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x103 ha y30e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x124 h7 y30d ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 xb9 ha y30e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x135 h7 y30d ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff8">ab<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">bc<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">ca<span class="ff6">)<span class="_ _c"> </span>¿p<span class="_ _24"></span>or<span class="_ _c"> </span>qu´<span class="_ _d"></span>e?</span></span></div><div class="t m0 x7c h7 y30f ff6 fs3 fc0 sc0 ls0 ws0">ejemplo<span class="_ _c"> </span>3)<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x46 ha y310 ff9 fs4 fc0 sc0 ls0 ws0">4</div><div class="t m0 x119 h7 y30f ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>4</div><div class="t m0 x7c h7 y311 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x8f ha y312 ff9 fs4 fc0 sc0 ls0 ws0">4</div><div class="t m0 x9b h7 y311 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>4<span class="ff8">a</span></div><div class="t m0 x4f ha y312 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa6 h7 y311 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>4<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>4<span class="ff8">a</span></div><div class="t m0 x103 ha y312 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7c h7 y313 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a</span></div><div class="t m0 x81 ha y314 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x85 h7 y313 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>2)</div><div class="t m0 x45 ha y314 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x34 h7 y313 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff6">4<span class="ff8">a</span></span></div><div class="t m0 x122 ha y314 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7c h7 y315 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span>(<span class="ff8">a</span></div><div class="t m0 x81 ha y316 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x85 h7 y315 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span>2<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>2)(<span class="ff8">a</span></div><div class="t m0 x8e ha y316 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x136 h7 y315 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff6">2<span class="ff8">a<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span>2)</span></div><div class="t m0 xa h7 y317 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Polin<span class="_ _12"></span>omios</div><div class="t m0 x21 h7 y318 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>T<span class="_ _10"></span>eorema<span class="_"> </span>del<span class="_"> </span>resto:<span class="_"> </span>Al<span class="_ _1e"> </span>dividir<span class="_"> </span>un<span class="_"> </span>p<span class="_ _24"></span>olinomio<span class="_"> </span>de<span class="_"> </span>grado<span class="_ _1e"> </span><span class="ff8">n<span class="_ _20"> </span></span>p<span class="_ _24"></span>or<span class="_"> </span>un<span class="_"> </span>binomio<span class="_ _21"> </span>de<span class="_"> </span>la<span class="_"> </span>forma</div><div class="t m0 x5f h7 y319 ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">x<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a</span>)<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">P<span class="_ _29"> </span><span class="ff6">(</span>x<span class="ff6">)<span class="_"> </span>=<span class="_"> </span>(</span>x<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">a<span class="ff6">)</span>Q<span class="ff6">(</span>x<span class="ff6">)<span class="_ _1e"> </span>+<span class="_ _1e"> </span></span>R<span class="ff6">,<span class="_ _c"> </span>donde<span class="_ _f"> </span></span>R<span class="_ _c"> </span><span class="ff6">es<span class="_ _c"> </span>un<span class="_ _c"> </span>#<span class="_ _c"> </span>real</span></span></span></div><div class="t m0 x7c h7 y31a ff6 fs3 fc0 sc0 ls0 ws0">Si<span class="_ _e"> </span><span class="ff8">R<span class="_ _20"> </span></span>=<span class="_"> </span>0<span class="_"> </span>=<span class="_ _4"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _33"> </span></span>−<span class="_ _33"></span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _20"> </span><span class="ff8">P<span class="_ _29"> </span><span class="ff6">(</span>x<span class="ff6">)<span class="_ _c"> </span>y<span class="_ _c"> </span>“</span>a<span class="ff6">”<span class="_ _e"> </span>es<span class="_ _c"> </span>un<span class="_ _c"> </span>divisor<span class="_ _e"> </span>del<span class="_ _c"> </span>t´<span class="_ _a"></span>ermino<span class="_ _e"> </span>indep<span class="_ _24"></span>endiente<span class="_ _e"> </span>de<span class="_ _e"> </span><span class="ff8">P<span class="_ _1f"> </span></span>(<span class="ff8">x</span>)</span></span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf16" class="pf w0 h0" data-page-no="16"><div class="pc pc16 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">19</div><div class="t m0 x21 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>T<span class="_ _10"></span>eorema<span class="_ _c"> </span>de<span class="_ _e"> </span>Bezout:<span class="_ _c"> </span>El<span class="_ _c"> </span>resto<span class="_ _c"> </span><span class="ff8">R<span class="_ _c"> </span></span>en<span class="_ _e"> </span>la<span class="_ _c"> </span>nota<span class="_ _c"> </span>an<span class="_ _12"></span>terior<span class="_ _e"> </span>es<span class="_ _c"> </span>igual<span class="_ _c"> </span>al<span class="_ _e"> </span>v<span class="_ _3"></span>alor<span class="_ _c"> </span>de<span class="_ _e"> </span><span class="ff8">P<span class="_ _1f"> </span></span>(<span class="ff8">x</span>)<span class="_ _e"> </span>para</div><div class="t m0 x5f h7 y81 ff8 fs3 fc0 sc0 ls0 ws0">x<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>a<span class="ff6">,<span class="_ _c"> </span>o<span class="_ _c"> </span>sea<span class="_ _c"> </span></span>R<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span></span>P<span class="_ _29"> </span><span class="ff6">(</span>a<span class="ff6">).<span class="_ _c"> </span>V<span class="_ _b"></span>er<span class="_ _f"> </span>regla<span class="_ _e"> </span>de<span class="_ _c"> </span>Ruffini</span></div><div class="t m0 x21 h7 y2a2 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">P<span class="_ _27"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">x</span></div><div class="t m0 x80 he y31b ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8b h7 y2a2 ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x2f he y31b ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x122 h7 y2a2 ff6 fs3 fc0 sc0 ls0 ws0">siempre<span class="_ _c"> </span>es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>(<span class="ff8">x<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>a</span>),<span class="_ _c"> </span><span class="ff8">n<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">N</span></span></span></div><div class="t m0 x21 h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">P<span class="_ _27"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">x</span></div><div class="t m0 x80 he y31c ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8b h7 y2cb ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x2f he y31c ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x122 h7 y2cb ff6 fs3 fc0 sc0 ls0 ws0">es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>(<span class="ff8">x<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span>),<span class="_ _c"> </span>si<span class="_ _c"> </span><span class="ff8">n<span class="_ _c"> </span></span>es<span class="_ _c"> </span>par</div><div class="t m0 x21 h7 y2cd ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">P<span class="_ _27"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">x</span></div><div class="t m0 x80 he y31d ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8b h7 y2cd ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x2f he y31d ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x122 h7 y2cd ff6 fs3 fc0 sc0 ls0 ws0">es<span class="_ _c"> </span>divisible<span class="_ _c"> </span>p<span class="_ _24"></span>or<span class="_ _c"> </span>(<span class="ff8">x<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span>),<span class="_ _c"> </span>si<span class="_ _c"> </span><span class="ff8">n<span class="_ _c"> </span></span>es<span class="_ _c"> </span>impar</div><div class="t m0 x21 h7 y31e ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Un<span class="_ _e"> </span>#<span class="_ _c"> </span><span class="ff8">x</span></div><div class="t m0 x9c ha y31f ff9 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 xaf h7 y31e ff6 fs3 fc0 sc0 ls0 ws0">es<span class="_ _c"> </span>la<span class="_ _c"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ız<span class="_ _c"> </span>de<span class="_ _c"> </span><span class="ff8">P<span class="_ _29"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">x</span></span></div><div class="t m0 xb7 ha y31f ff9 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12a h7 y31e ffa fs3 fc0 sc0 ls0 ws0">|<span class="_ _20"> </span><span class="ff8">P<span class="_ _29"> </span><span class="ff6">(</span>x<span class="ff6">)</span></span></div><div class="t m0 x21 h7 y320 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>T<span class="_ _10"></span>eorema<span class="_ _c"> </span>de<span class="_ _c"> </span>Vieta</div><div class="t m0 x7c h7 y2a8 ff6 fs3 fc0 sc0 ls0 ws0">Sea<span class="_ _c"> </span><span class="ff8">P<span class="_ _29"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">x</span></div><div class="t m0 x6a he y321 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x47 h7 y2a8 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 xae ha y322 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x104 h9 y2a8 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x51 ha y321 ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x137 h7 y2a8 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 xdc ha y322 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x84 h9 y2a8 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x9 ha y321 ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">2</span></span></div><div class="t m0 x138 h7 y2a8 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x139 ha y322 ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x123 h7 y2a8 ff8 fs3 fc0 sc0 ls0 ws0">x<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>a</div><div class="t m0 x13a he y322 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7c h7 y323 ff6 fs3 fc0 sc0 ls0 ws0">con<span class="_ _c"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ıces<span class="_ _c"> </span><span class="ff8">x</span></div><div class="t m0 x34 ha y324 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa7 h9 y323 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>x</div><div class="t m0 x6b ha y324 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x13b h9 y323 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>...,<span class="_ _1f"> </span>x</div><div class="t m0 x124 he y324 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x13c h7 y323 ff6 fs3 fc0 sc0 ls0 ws0">cumple<span class="_ _c"> </span>con:</div><div class="t m0 x7c h9 y325 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xb0 ha y326 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x42 h7 y325 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 xbd ha y326 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x13d h7 y325 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x13b ha y326 ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x9e h7 y325 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 xf0 he y326 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x13e h7 y325 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ffa">−<span class="ff8">a</span></span></div><div class="t m0 x13f ha y326 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x7c h9 y327 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xb0 ha y328 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x31 h9 y327 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x8f ha y328 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9b h7 y327 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x44 ha y328 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4f h9 y327 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x8b ha y328 ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x46 h7 y327 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x51 ha y328 ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x12e h9 y327 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x82 he y328 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x83 h7 y327 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x13f ha y328 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7c h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xb0 ha y32a ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x31 h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x8f ha y32a ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4d h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x140 ha y32a ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xf7 h7 y329 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x8b ha y32a ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x34 h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x20 ha y32a ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2f h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x4 ha y32a ff9 fs4 fc0 sc0 ls0 ws0">4</div><div class="t m0 x8d h7 y329 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x82 ha y32a ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">2</span></span></div><div class="t m0 x6 h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x131 ha y32a ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff7">−<span class="ff9">1</span></span></div><div class="t m0 x141 h9 y329 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x3e he y32a ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x55 h7 y329 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ffa">−<span class="ff8">a</span></span></div><div class="t m0 x5d ha y32a ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 x7c h7 y32b ffa fs3 fc0 sc0 ls0 ws0">·</div><div class="t m0 x7c h7 y32c ffa fs3 fc0 sc0 ls0 ws0">·</div><div class="t m0 x7c h7 y32d ffa fs3 fc0 sc0 ls0 ws0">·</div><div class="t m0 x7c h9 y32e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xb0 ha y32f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x31 h9 y32e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x8f ha y32f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4d h9 y32e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x140 ha y32f ff9 fs4 fc0 sc0 ls0 ws0">3</div><div class="t m0 xf7 h7 y32e ffa fs3 fc0 sc0 ls0 ws0">·<span class="_ _1e"> </span>·<span class="_ _1e"> </span>·<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x133 he y32f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x119 h7 y32e ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ffa">−<span class="ff8">a</span></span></div><div class="t m0 x10 he y32f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x3c h7 y32e ff6 fs3 fc0 sc0 ls0 ws0">(si<span class="_ _c"> </span><span class="ff8">n<span class="_ _c"> </span></span>es<span class="_ _c"> </span>impar)</div><div class="t m0 x119 h7 y330 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x8e he y331 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x124 h7 y330 ff6 fs3 fc0 sc0 ls0 ws0">(si<span class="_ _c"> </span><span class="ff8">n<span class="_ _c"> </span></span>es<span class="_ _c"> </span>par)</div><div class="t m0 x7c h7 y332 ff6 fs3 fc0 sc0 ls0 ws0">En<span class="_ _c"> </span>particular<span class="_ _c"> </span><span class="ff8">P<span class="_ _29"> </span></span>(<span class="ff8">x</span>)<span class="_"> </span>=<span class="_"> </span><span class="ff8">x</span></div><div class="t m0 x13c ha y333 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x137 h7 y332 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">px<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">q<span class="_ _e"> </span></span>=<span class="_"> </span>(<span class="ff8">x<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>x</span></div><div class="t m0 x139 ha y334 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xcb h7 y332 ff6 fs3 fc0 sc0 ls0 ws0">)(<span class="ff8">x<span class="_ _1e"> </span><span class="ffa">−<span class="_ _1e"> </span></span>x</span></div><div class="t m0 xd7 ha y334 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xef h7 y332 ff6 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 x4 h9 y335 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xe3 ha y336 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xf4 h7 y335 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 xb5 ha y336 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7e h7 y335 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ffa">−<span class="ff8">p<span class="_ _c"> </span></span></span>y<span class="_ _c"> </span><span class="ff8">x</span></div><div class="t m0 x11e ha y336 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x142 h9 y335 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 xcd ha y336 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x15 h7 y335 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">q</span></div><div class="t m0 x7c h7 y337 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span>en<span class="_ _c"> </span><span class="ff8">ax</span></div><div class="t m0 x69 ha y338 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12 h7 y337 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">bx<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">c<span class="_ _20"> </span></span>=<span class="_"> </span>0<span class="_ _c"> </span>la<span class="_ _c"> </span>ecuaci´<span class="_ _d"></span>on<span class="_ _c"> </span>tiene<span class="_ _f"> </span>2<span class="_ _e"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ıces<span class="_ _c"> </span>reales<span class="_ _c"> </span>si<span class="_ _f"> </span><span class="ff8">D<span class="_ _20"> </span>><span class="_ _20"> </span></span>0</div><div class="t m0 x98 h7 y339 ff6 fs3 fc0 sc0 ls0 ws0">no<span class="_ _c"> </span>tiene<span class="_ _c"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ıces<span class="_ _c"> </span>reales<span class="_ _c"> </span>si<span class="_ _c"> </span><span class="ff8">D<span class="_ _e"> </span><<span class="_ _20"> </span></span>0</div><div class="t m0 x98 h7 y33a ff6 fs3 fc0 sc0 ls0 ws0">tiene<span class="_ _c"> </span>una<span class="_ _c"> </span>sola<span class="_ _c"> </span>ra<span class="_ _10"></span>´<span class="_ _11"></span>ız<span class="_ _c"> </span>si<span class="_ _c"> </span><span class="ff8">D<span class="_ _e"> </span></span>=<span class="_"> </span>0</div><div class="t m0 x7c h7 y2de ff8 fs3 fc0 sc0 ls0 ws0">D<span class="_ _e"> </span><span class="ff6">=<span class="_"> </span></span>b</div><div class="t m0 x140 ha y33b ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x69 h7 y2de ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span><span class="ff6">4<span class="ff8">ac<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">x</span></span></div><div class="t m0 x8d ha y33c ff9 fs4 fc0 sc0 ls0 ws0">1<span class="ffd">,</span>2</div><div class="t m0 x9e h7 y2de ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xd0 h7 y33d ffa fs3 fc0 sc0 ls0 ws0">−<span class="ff8">b<span class="_ _1e"> </span></span>±</div><div class="t m0 xdc h7 y33e ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x131 h9 y33d ff8 fs3 fc0 sc0 ls0 ws0">D</div><div class="t m0 x11d h7 y33f ff6 fs3 fc0 sc0 ls0 ws0">2<span class="ff8">a</span></div><div class="t m0 xa h7 y340 ff6 fs3 fc0 sc0 ls0 ws0">3<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Desigualdades.<span class="_ _c"> </span>Si<span class="_ _c"> </span><span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c<span class="_ _20"> </span><span class="ffa">∈<span class="_ _20"> </span><span class="ff10">R</span></span></span></div><div class="t m0 x21 h7 y341 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><<span class="_ _20"> </span>b<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a<span class="_ _1e"> </span></span>±<span class="_ _1e"> </span><span class="ff8">c<span class="_ _20"> </span><<span class="_ _20"> </span>b<span class="_ _1e"> </span></span>±<span class="_ _1e"> </span><span class="ff8">c</span></span></div><div class="t m0 x21 h7 y342 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span>0<span class="_"> </span><span class="ff8"><<span class="_ _20"> </span>a<span class="_ _20"> </span><<span class="_ _20"> </span>b<span class="_ _20"> </span></span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 xf he y343 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x48 h9 y342 ff8 fs3 fc0 sc0 ls0 ws0"><<span class="_ _20"> </span>b</div><div class="t m0 x13c he y343 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x21 h7 y344 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">a<span class="_ _21"> </span><<span class="_ _20"> </span>b<span class="_ _20"> </span><<span class="_ _20"> </span></span>0<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 x4 he y345 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x13 h9 y344 ff8 fs3 fc0 sc0 ls0 ws0"><<span class="_ _20"> </span>b</div><div class="t m0 x51 he y345 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xb4 h7 y344 ffa fs3 fc0 sc0 ls0 ws0">⇐<span class="_ _2a"></span>⇒<span class="_ _20"> </span><span class="ff8">n<span class="_ _c"> </span><span class="ff6">es<span class="_ _c"> </span>impar</span></span></div><div class="t m0 x21 h7 y346 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><<span class="_ _20"> </span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">c<span class="_ _20"> </span>><span class="_ _20"> </span></span>0<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">ac<span class="_ _20"> </span><<span class="_ _20"> </span>bc</span></span></div><div class="t m0 x21 h7 y347 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>si<span class="_ _e"> </span><span class="ff8">a<span class="_ _20"> </span><<span class="_ _20"> </span>b<span class="_ _c"> </span></span>y<span class="_ _c"> </span><span class="ff8">c<span class="_ _20"> </span><<span class="_ _20"> </span></span>0<span class="_"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">ac<span class="_ _20"> </span>><span class="_ _20"> </span>bc</span></span></div><div class="t m0 x21 h7 y348 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ff8">a</span></div><div class="t m0 xb0 ha y349 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x143 h7 y348 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff6">0</span></div><div class="t m0 x21 h7 y34a ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a,<span class="_ _1f"> </span>b<span class="_ _c"> </span></span>tienen<span class="_ _c"> </span>suma<span class="_ _f"> </span>constan<span class="_ _3"></span>te<span class="_ _c"> </span>=<span class="_ _2a"></span><span class="ffa">⇒<span class="_ _20"> </span><span class="ff8">ab<span class="_ _c"> </span><span class="ff6">es<span class="_ _c"> </span>m´<span class="_ _a"></span>aximo<span class="_ _c"> </span>si<span class="_ _c"> </span><span class="ff8">a<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">b</span></span></span></span></div><div class="t m0 xcc h7 y34b ffa fs3 fc0 sc0 ls0 ws0">−<span class="_ _1e"> </span>·<span class="_ _1e"> </span>−<span class="_ _1e"> </span>·<span class="_ _1e"> </span>−</div><div class="t m0 x21 h7 y34c ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x<span class="_ _20"> </span></span>|<span class="_ _c"> </span>≥<span class="_ _20"> </span></span>0<span class="_ _c"> </span>con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>0</span></span></span></div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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"/><div class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">20</div><div class="t m0 x21 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x<span class="_ _20"> </span></span>|<span class="_ _c"> </span>≥<span class="_ _20"> </span><span class="ff8">x<span class="_ _c"> </span></span></span>con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff6">0</span></span></div><div class="t m0 x21 h7 y2a1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x<span class="_ _20"> </span></span>|<span class="_ _c"> </span></span>=<span class="_ _c"> </span><span class="ffa">|<span class="_ _20"> </span>−<span class="ff8">x<span class="_ _20"> </span></span>|</span></div><div class="t m0 x21 h7 y2c7 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">xy<span class="_ _c"> </span></span>|<span class="_ _c"> </span></span>=<span class="_ _c"> </span><span class="ffa">|<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>||<span class="_ _20"> </span><span class="ff8">y<span class="_ _e"> </span></span>|</span></div><div class="t m0 x21 h7 y34d ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x<span class="_ _20"> </span></span>|<span class="_ _c"> </span>≤<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>⇐<span class="_ _2a"></span>⇒<span class="_ _20"> </span>−<span class="ff8">a<span class="_ _20"> </span></span>≤<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>≤<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 x21 h7 y34e ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x<span class="_ _20"> </span></span>|<span class="_ _c"> </span>≥<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>⇐<span class="_ _2a"></span>⇒<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">a<span class="_ _c"> </span><span class="ff6">o<span class="_ _c"> </span></span>x<span class="_ _20"> </span></span>≤<span class="_ _20"> </span>−<span class="ff8">a</span></span></div><div class="t m0 x21 h7 y34f ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">x</span></span></div><div class="t m0 x42 ha y350 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x106 h7 y34f ffa fs3 fc0 sc0 ls0 ws0">|<span class="_ _c"> </span><span class="ff6">=<span class="_ _c"> </span></span>|<span class="_ _20"> </span><span class="ff8">x<span class="_ _20"> </span></span>|</div><div class="t m0 x34 ha y350 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xac h7 y34f ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _c"> </span><span class="ff8">x</span></div><div class="t m0 x8e ha y350 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x21 h7 y351 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">a<span class="_ _1e"> </span></span></span>+<span class="_ _1e"> </span><span class="ff8">b<span class="_ _20"> </span><span class="ffa">|<span class="_ _c"> </span>≤<span class="_ _c"> </span>|<span class="_ _20"> </span></span>a<span class="_ _20"> </span><span class="ffa">|<span class="_ _c"> </span></span></span>+<span class="_ _c"> </span><span class="ffa">|<span class="_ _20"> </span><span class="ff8">b<span class="_ _20"> </span></span>|<span class="_ _c"> </span></span>con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">ab<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>0</span></span></span></div><div class="t m0 x21 h7 y352 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span><span class="ffa">|<span class="_ _21"> </span><span class="ff8">a<span class="_ _1e"> </span></span>−<span class="_ _1e"> </span><span class="ff8">b<span class="_ _20"> </span></span>|<span class="_ _c"> </span>≥<span class="_ _c"> </span>|<span class="_ _20"> </span><span class="ff8">a<span class="_ _20"> </span></span>|<span class="_ _c"> </span>−<span class="_ _c"> </span>|<span class="_ _20"> </span><span class="ff8">b<span class="_ _20"> </span></span>|<span class="_ _c"> </span></span>con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _4"></span>⇒<span class="_ _20"> </span><span class="ff8">ab<span class="_ _20"> </span><span class="ff6">=<span class="_"> </span>0</span></span></span></div><div class="t m0 xa h7 y353 ff6 fs3 fc0 sc0 ls0 ws0">4<span class="_ _28"></span><span class="ffa">·<span class="_ _27"></span></span>-<span class="_ _c"> </span>Desigualdades<span class="_ _c"> </span>Notables</div><div class="t m0 x21 h7 y354 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Relaci´<span class="_ _d"></span>on<span class="_ _c"> </span>entre<span class="_ _e"> </span>las<span class="_ _c"> </span>medias:<span class="_ _c"> </span><span class="ff8">R<span class="_ _20"> </span><span class="ffa">≥<span class="_ _20"> </span></span>A<span class="_ _20"> </span><span class="ffa">≥<span class="_ _20"> </span></span>g<span class="_ _e"> </span><span class="ffa">≥<span class="_ _20"> </span></span>H<span class="_ _28"></span></span>,<span class="_ _c"> </span>o<span class="_ _c"> </span>sea,</div><div class="t m0 x7c hb y355 ffb fs3 fc0 sc0 ls0 ws0">r</div><div class="t m0 x144 h9 y356 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 xa3 ha y357 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa3 ha y358 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe2 h7 y356 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x44 ha y357 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x44 ha y358 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x45 h7 y356 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...a</span></div><div class="t m0 x4 ha y357 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x4 he y359 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x12 h9 y35a ff8 fs3 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7e h7 y35b ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x105 he y35c ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xcf hb y35d ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xad ha y35e ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x63 h9 y356 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x98 he y35f ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x134 h9 y35a ff8 fs3 fc0 sc0 ls0 ws0">n</div><div class="t m0 x56 h7 y35b ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x132 h12 y360 ff12 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m0 xcb hb y361 ffb fs3 fc0 sc0 ls0 ws0">s</div><div class="t m0 x59 he y35c ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xbb hb y35d ffb fs3 fc0 sc0 ls0 ws0">Q</div><div class="t m0 x10d ha y35e ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 xc4 h9 y362 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x12f he y363 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xdb h7 y362 ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x116 h9 y356 ff8 fs3 fc0 sc0 ls0 ws0">n</div><div class="t m0 x111 he y364 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xea hb y365 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 xea ha y366 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=</span>i</div><div class="t m0 x145 h7 y367 ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 xfd h9 y368 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x28 he y369 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7c h7 y36a ff6 fs3 fc0 sc0 ls0 ws0">Ra<span class="_ _10"></span>´<span class="_ _11"></span>ız<span class="_ _c"> </span>cuadrada<span class="_ _c"> </span>de<span class="_ _c"> </span>la<span class="_ _3c"> </span><span class="ffa">≥<span class="_ _3b"> </span></span>Media<span class="_ _3c"> </span><span class="ffa">≥<span class="_ _3c"> </span></span>Media<span class="_ _3b"> </span><span class="ffa">≥<span class="_ _3c"> </span></span>Media</div><div class="t m0 xd1 h7 y36b ff6 fs3 fc0 sc0 ls0 ws0">media<span class="_ _c"> </span>aritm<span class="_ _12"></span>´<span class="_ _a"></span>etica<span class="_ _3d"> </span>aritm<span class="_ _3"></span>´<span class="_ _25"></span>etica<span class="_ _3e"> </span>geom<span class="_ _3"></span>´<span class="_ _25"></span>etrica<span class="_ _3f"> </span>arm´<span class="_ _d"></span>onica</div><div class="t m0 xc5 h7 y36c ff6 fs3 fc0 sc0 ls0 ws0">de<span class="_ _c"> </span>los<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x2f he y36d ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7c h7 y36e ff6 fs3 fc0 sc0 ls0 ws0">siendo<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x32 ha y36f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x80 h9 y36e ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>a</div><div class="t m0 x5b ha y36f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x46 h9 y36e ff8 fs3 fc0 sc0 ls0 ws0">...a</div><div class="t m0 x4 he y36f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x13 h7 y36e ff8 fs3 fc0 sc0 ls0 ws0">><span class="_ _20"> </span><span class="ff6">0</span></div><div class="t m0 x7c h7 y370 ff6 fs3 fc0 sc0 ls0 ws0">Con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _2a"></span>⇒<span class="_ _20"> </span><span class="ff8">a</span></span></div><div class="t m0 x6a ha y371 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xf8 h7 y370 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 xae ha y371 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9e h7 y370 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">...<span class="_ _20"> </span></span>=<span class="_"> </span><span class="ff8">a</span></div><div class="t m0 x6 he y371 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7c h7 y372 ff6 fs3 fc0 sc0 ls0 ws0">En<span class="_ _c"> </span>particular</div><div class="t m0 x7c h7 y373 ff6 fs3 fc0 sc0 ls0 ws0">para<span class="_ _c"> </span><span class="ff8">a,<span class="_ _1f"> </span>b,<span class="_ _1f"> </span>c<span class="_ _20"> </span>><span class="_ _20"> </span></span>0:</div><div class="t m0 x9d hb y374 ffb fs3 fc0 sc0 ls0 ws0">r</div><div class="t m0 xf4 h9 y375 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x104 ha y376 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3c h7 y375 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x146 ha y376 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x135 h7 y375 ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">c</span></div><div class="t m0 x84 ha y376 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x147 h7 y377 ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 x62 h7 y373 ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x148 h7 y375 ff8 fs3 fc0 sc0 ls0 ws0">a<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>b<span class="_ _1e"> </span><span class="ff6">+<span class="_ _1e"> </span></span>c</div><div class="t m0 x72 h7 y377 ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 xc0 h7 y373 ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x123 h11 y378 ff11 fs7 fc0 sc0 ls0 ws0">3</div><div class="t m0 x10d h7 y379 ffa fs3 fc0 sc0 ls0 ws0">√</div><div class="t m0 x26 h7 y373 ff8 fs3 fc0 sc0 ls0 ws0">abc<span class="_ _20"> </span><span class="ffa">≥</span></div><div class="t m0 x127 h7 y375 ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 xe0 h7 y37a ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe0 h9 y37b ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x113 h7 y37c ff6 fs3 fc0 sc0 ls0 ws0">+</div><div class="t m0 x127 h7 y37a ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x127 h9 y37b ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xea h7 y37c ff6 fs3 fc0 sc0 ls0 ws0">+</div><div class="t m0 x1b h7 y37a ff6 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x1b h9 y37b ff8 fs3 fc0 sc0 ls0 ws0">c</div><div class="t m0 x21 h7 y37d ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Cauc<span class="_ _3"></span>hy<span class="_ _e"> </span>Sch<span class="_ _3"></span>w<span class="_ _3"></span>artz</div><div class="t m0 x7c h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a</span></div><div class="t m0 xd1 ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd1 ha y380 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x8f h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 xa8 ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa8 ha y380 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2d h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x36 ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x36 he y381 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x149 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">)(<span class="ff8">b</span></div><div class="t m0 xe7 ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe7 ha y380 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x49 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x82 ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x82 ha y380 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x39 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">b</span></div><div class="t m0 x3e ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3e he y381 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">)<span class="_"> </span><span class="ffa">≥<span class="_ _20"> </span></span>(<span class="ff8">a</span></div><div class="t m0 x5d ha y382 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x109 h9 y37e ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x57 ha y382 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa9 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x11c ha y382 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10b h9 y37e ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xd7 ha y382 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x16 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x12b he y382 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x111 h9 y37e ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x116 he y382 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc3 h7 y37e ff6 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 xee ha y37f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x7c h7 y383 ff6 fs3 fc0 sc0 ls0 ws0">siendo<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x32 ha y384 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x80 h9 y383 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>a</div><div class="t m0 x5b ha y384 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x46 h9 y383 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>...,<span class="_ _1f"> </span>a</div><div class="t m0 x8e he y384 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xae h9 y383 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>b</div><div class="t m0 xe7 ha y384 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xb2 h9 y383 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>b</div><div class="t m0 xf0 ha y384 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb9 h9 y383 ff8 fs3 fc0 sc0 ls0 ws0">...,<span class="_ _1f"> </span>b</div><div class="t m0 x130 he y384 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x105 h7 y383 ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R</span></div><div class="t m0 x7c h7 y385 ff6 fs3 fc0 sc0 ls0 ws0">Con<span class="_ _c"> </span>=<span class="_ _c"> </span><span class="ffa">⇐<span class="_ _2a"></span>⇒</span></div><div class="t m0 x46 h9 y386 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 xac ha y387 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2e h9 y388 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x6a ha y389 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x4 h7 y385 ff6 fs3 fc0 sc0 ls0 ws0">=</div><div class="t m0 xf h9 y386 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x37 ha y387 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf h9 y388 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x10 ha y389 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3c h7 y385 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_"> </span><span class="ff8">...<span class="_ _20"> </span></span>=</div><div class="t m0 x6 h9 y386 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x131 he y387 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x53 h9 y388 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x14a he y389 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7c h7 y38a ff6 fs3 fc0 sc0 ls0 ws0">Adem´<span class="_ _d"></span>as<span class="_ _c"> </span>se<span class="_ _c"> </span>cumple:</div><div class="t m0 x9e h9 y38b ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x124 ha y38c ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x124 ha y38d ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x9e h9 y38e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x38 ha y38f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xb3 h7 y38a ff6 fs3 fc0 sc0 ls0 ws0">+</div><div class="t m0 x52 h9 y38b ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x39 ha y38c ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x39 ha y38d ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x14b h9 y38e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x39 ha y38f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6 h7 y38a ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+</div><div class="t m0 x54 h9 y38b ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 xe4 ha y38c ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xe4 he y390 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x54 h9 y38e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x14c he y38f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x56 h7 y38a ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x5d h7 y38b ff6 fs3 fc0 sc0 ls0 ws0">(<span class="ff8">a</span></div><div class="t m0 x57 ha y391 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa9 h7 y38b ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x11c ha y391 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x14d h7 y38b ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">a</span></div><div class="t m0 x19 he y391 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x91 h7 y38b ff6 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 x14e ha y38c ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x14f h9 y38e ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x58 ha y38f ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x10d h7 y38e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x10e ha y38f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10f h7 y38e ff6 fs3 fc0 sc0 ls0 ws0">+<span class="_ _1e"> </span><span class="ff8">...<span class="_ _1e"> </span></span>+<span class="_ _1e"> </span><span class="ff8">x</span></div><div class="t m0 x150 he y38f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7c h7 y392 ff6 fs3 fc0 sc0 ls0 ws0">siendo<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x32 ha y393 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x80 h9 y392 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>a</div><div class="t m0 x5b ha y393 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x46 h9 y392 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>...a</div><div class="t m0 x3b he y393 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf h7 y392 ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R<span class="_ _c"> </span><span class="ff6">y<span class="_ _c"> </span><span class="ff8">x</span></span></span></div><div class="t m0 x135 ha y393 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x151 h9 y392 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>x</div><div class="t m0 xad ha y393 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9 h9 y392 ff8 fs3 fc0 sc0 ls0 ws0">,<span class="_ _1f"> </span>...,<span class="_ _1f"> </span>x</div><div class="t m0 x71 he y393 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x152 h7 y392 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff6">0</span></div><div class="t m0 x7c h7 y394 ff6 fs3 fc0 sc0 ls0 ws0">Esta<span class="_ _c"> </span>forma<span class="_ _c"> </span>es<span class="_ _c"> </span>muy<span class="_ _e"> </span>“atractiv<span class="_ _3"></span>a”<span class="_ _c"> </span>y<span class="_ _c"> </span>se<span class="_ _c"> </span>cono<span class="_ _24"></span>ce<span class="_ _c"> </span>como<span class="_ _c"> </span>Desigualdad<span class="_ _c"> </span>de<span class="_ _f"> </span>Arth<span class="_ _3"></span>ur<span class="_ _c"> </span>Engels</div><div class="t m0 x21 h7 y395 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Reacomodo</div><div class="t m0 xc6 he y396 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x22 hb y397 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x7c ha y398 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x2b h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x81 he y39a ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x153 h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x85 he y39a ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x69 h7 y399 ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 x154 he y396 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x79 hb y397 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x33 ha y398 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 xb1 h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x2f he y39b ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x47 h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xf2 he y39b ffd fs4 fc0 sc0 ls0 ws0">γ</div><div class="t m0 xe3 h12 y39c ff12 fs7 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf h7 y399 ffa fs3 fc0 sc0 ls0 ws0">≥</div><div class="t m0 xb2 he y396 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xf3 hb y397 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x51 ha y398 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x155 h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x156 he y39b ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x52 h9 y399 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x39 ha y39b ffd fs4 fc0 sc0 ls0 ws0">n<span class="ff9">+1<span class="ff7">−</span></span>i</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
<div id="pf18" class="pf w0 h0" data-page-no="18"><div class="pc pc18 w0 h0"><img class="bi x0 y0 w1 h1" alt="" 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class="t m0 xe1 h7 y8 ff6 fs3 fc0 sc0 ls0 ws0">21</div><div class="t m0 x7c h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">con<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 xe2 he y19f ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc5 h7 y9 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 x45 ha y19f ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x34 h7 y9 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 xe7 he y19f ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 xb2 h7 y9 ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 x12e he y19f ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x14b h7 y9 ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R</span></div><div class="t m0 x7c h9 y39d ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xc6 he y39e ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x31 h7 y39d ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x7a ha y39e ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf7 h7 y39d ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x157 he y39e ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x36 h7 y39d ff6 fs3 fc0 sc0 ls0 ws0">,<span class="_ _c"> </span><span class="ff8">b</span></div><div class="t m0 x10 he y39e ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xe7 h7 y39d ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R</span></div><div class="t m0 x7c h7 y39f ff8 fs3 fc0 sc0 ls0 ws0">γ<span class="_ _c"> </span><span class="ff6">=<span class="_"> </span><span class="ffa">{</span>1</span>,<span class="_ _1f"> </span><span class="ff6">2</span>,<span class="_ _1f"> </span>...n<span class="ffa">}<span class="_ _c"> </span><span class="ff6">cualquier<span class="_ _c"> </span>p<span class="_ _24"></span>ermutaci<span class="_ _4"></span>´<span class="_ _11"></span>ın<span class="_ _f"> </span>de<span class="_ _e"> </span><span class="ff8">a</span></span></span></div><div class="t m0 x3f he y3a0 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x66 h7 y39f ff6 fs3 fc0 sc0 ls0 ws0">,<span class="ff8">b</span></div><div class="t m0 x57 he y3a0 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x21 h7 y3a1 ff6 fs3 fc0 sc0 ls0 ws0">-<span class="_ _16"> </span>Sheb<span class="_ _3"></span>ychev</div><div class="t m0 x144 h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">·<span class="ff6">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a</span></span></div><div class="t m0 x12 ha y3a3 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x128 h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 x158 ha y3a3 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x157 h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 x12e he y3a3 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x11d h7 y3a2 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">b</span></div><div class="t m0 x84 ha y3a3 ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x13f h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x98 ha y3a3 ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x71 h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x159 he y3a3 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x10d h7 y3a2 ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R</span></div><div class="t m0 xa5 h7 y3a4 ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒</span></div><div class="t m0 xa7 he y3a5 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x133 hb y3a6 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x34 ha y3a7 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x47 h9 y3a4 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x122 he y3a8 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf he y3a5 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x117 hb y3a6 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x8e ha y3a7 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 xe7 h9 y3a4 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xb2 he y3a8 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xd0 h7 y3a4 ffa fs3 fc0 sc0 ls0 ws0">≤<span class="_ _20"> </span><span class="ff8">n</span></div><div class="t m0 xec he y3a5 ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x83 hb y3a6 ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x151 ha y3a7 ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x105 h9 y3a4 ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x15a he y3a8 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xfa h9 y3a4 ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x134 he y3a8 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x144 h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">·<span class="ff6">-<span class="_ _16"> </span>Si<span class="_ _e"> </span><span class="ff8">a</span></span></div><div class="t m0 x12 ha y3aa ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x128 h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 x158 ha y3aa ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x157 h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≥<span class="_ _20"> </span><span class="ff8">a</span></div><div class="t m0 x12e he y3aa ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x11d h7 y3a9 ff6 fs3 fc0 sc0 ls0 ws0">y<span class="_ _c"> </span><span class="ff8">b</span></div><div class="t m0 x84 ha y3aa ff9 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x13f h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">≤<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x98 ha y3aa ff9 fs4 fc0 sc0 ls0 ws0">2</div><div class="t m0 x71 h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">≤<span class="_ _20"> </span><span class="ff8">...<span class="_ _20"> </span></span>≤<span class="_ _20"> </span><span class="ff8">b</span></div><div class="t m0 x159 he y3aa ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x10d h7 y3a9 ffa fs3 fc0 sc0 ls0 ws0">∈<span class="_ _20"> </span><span class="ff10">R</span></div><div class="t m0 xa5 h7 y3ab ff6 fs3 fc0 sc0 ls0 ws0">=<span class="_ _2a"></span><span class="ffa">⇒</span></div><div class="t m0 xa7 he y3ac ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x133 hb y3ad ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x34 ha y3ae ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x47 h9 y3ab ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x122 he y3af ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf he y3ac ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x117 hb y3ad ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x8e ha y3ae ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 xe7 h9 y3ab ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 xb2 he y3af ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xd0 h7 y3ab ffa fs3 fc0 sc0 ls0 ws0">≥<span class="_ _20"> </span><span class="ff8">n</span></div><div class="t m0 xec he y3ac ffd fs4 fc0 sc0 ls0 ws0">n</div><div class="t m0 x83 hb y3ad ffb fs3 fc0 sc0 ls0 ws0">P</div><div class="t m0 x151 ha y3ae ffd fs4 fc0 sc0 ls0 ws0">i<span class="ff9">=1</span></div><div class="t m0 x105 h9 y3ab ff8 fs3 fc0 sc0 ls0 ws0">a</div><div class="t m0 x15a he y3af ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xfa h9 y3ab ff8 fs3 fc0 sc0 ls0 ws0">b</div><div class="t m0 x134 he y3af ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x9b h7 y3b0 ff6 fs3 fc0 sc0 ls0 ws0">Con<span class="_ _c"> </span>=<span class="_ _c"> </span>si<span class="_ _c"> </span>uno<span class="_ _c"> </span>de<span class="_ _c"> </span>los<span class="_ _c"> </span><span class="ff8">a</span></div><div class="t m0 xa0 he y3b1 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 x5 h7 y3b0 ff6 fs3 fc0 sc0 ls0 ws0">o<span class="_ _c"> </span><span class="ff8">b</span></div><div class="t m0 x62 he y3b1 ffd fs4 fc0 sc0 ls0 ws0">i</div><div class="t m0 xed h7 y3b0 ff6 fs3 fc0 sc0 ls0 ws0">es<span class="_ _c"> </span>constan<span class="_ _12"></span>te</div><div class="t m0 xd6 h7 y3b2 ff6 fs3 fc0 sc0 ls0 ws0">*<span class="_ _16"> </span>Estas<span class="_ _1e"> </span>2<span class="_ _1e"> </span>desigualdades<span class="_ _1e"> </span>son<span class="_ _21"> </span>tam<span class="_ _3"></span>bi´<span class="_ _a"></span>en<span class="_ _1e"> </span>muy<span class="_ _1e"> </span>“atractiv<span class="_ _b"></span>as”,<span class="_ _21"> </span>es<span class="_ _1e"> </span>p<span class="_ _24"></span>osible<span class="_ _21"> </span>que<span class="_ _1e"> </span>vistas<span class="_ _1e"> </span>as<span class="_ _10"></span>´<span class="_ _11"></span>ı<span class="_ _21"> </span>no<span class="_ _1e"> </span>se</div><div class="t m0 x5f h7 y3b3 ff6 fs3 fc0 sc0 ls0 ws0">en<span class="_ _3"></span>tiendan<span class="_"> </span>bien,<span class="_ _1e"> </span>p<span class="_ _24"></span>ero<span class="_"> </span>en<span class="_ _1e"> </span>la<span class="_ _21"> </span>Lecci´<span class="_ _d"></span>on<span class="_"> </span>#7<span class="_ _1e"> </span>las<span class="_"> </span>v<span class="_ _3"></span>eremos.<span class="_ _21"> </span>Igualmen<span class="_ _12"></span>te<span class="_ _21"> </span>existen<span class="_ _1e"> </span>otras<span class="_"> </span>desigual-</div><div class="t m0 x5f h7 y3b4 ff6 fs3 fc0 sc0 ls0 ws0">dades<span class="_ _c"> </span>notables<span class="_ _c"> </span>que<span class="_ _c"> </span>en<span class="_ _c"> </span>otro<span class="_ _c"> </span>momen<span class="_ _3"></span>to<span class="_ _c"> </span>notificaremos.<span class="_ _c"> </span>Por<span class="_ _e"> </span>ahora<span class="_ _c"> </span>estas<span class="_ _c"> </span>que<span class="_ _c"> </span>mostramos</div><div class="t m0 x5f h7 y3b5 ff6 fs3 fc0 sc0 ls0 ws0">resultan<span class="_ _c"> </span>una<span class="_ _c"> </span>herramienta<span class="_ _e"> </span>p<span class="_ _24"></span>o<span class="_ _24"></span>derosa<span class="_ _c"> </span>para<span class="_ _c"> </span>resolver<span class="_ _e"> </span>problemas<span class="_ _c"> </span>de<span class="_ _c"> </span>desigualdades.</div><div class="t m0 x7c h7 y3b6 ff6 fs3 fc0 sc0 ls0 ws0">Con<span class="_ _3"></span>tinuamos<span class="_ _e"> </span>pr´<span class="_ _a"></span>oximamen<span class="_ _3"></span>te.</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div>
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