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Algunos problemas con triángulos - Historial de revisiones
2024-03-29T08:59:33Z
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Manueljjaen: /* Problema I */
2012-03-09T18:19:03Z
<p><span class="autocomment">Problema I</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 18:19 9 mar 2012</td>
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<tr><td colspan="2" class="diff-lineno">Línea 14:</td>
<td colspan="2" class="diff-lineno">Línea 14:</td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Otra solución se basaría en la propiedad</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema II==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema II==</div></td></tr>
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Manueljjaen
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=25938&oldid=prev
Manueljjaen: /* Problema I */
2012-03-09T18:18:37Z
<p><span class="autocomment">Problema I</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 18:18 9 mar 2012</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Otra solución se basaría en la propiedad</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema II==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema II==</div></td></tr>
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Manueljjaen
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24428&oldid=prev
EduardoRamos: Deshacer vandalismo
2011-09-20T08:25:20Z
<p>Deshacer vandalismo</p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 08:25 20 sep 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Hey, subtle must be your mildde name. Great post!</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema II==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">OQZryW </del><<del style="color: red; font-weight: bold; text-decoration: none;">a href</del>=<del style="color: red; font-weight: bold; text-decoration: none;">"http:</del>//<del style="color: red; font-weight: bold; text-decoration: none;">zebbeirbggfp.com</del>/<del style="color: red; font-weight: bold; text-decoration: none;">"</del>><del style="color: red; font-weight: bold; text-decoration: none;">zebbeirbggfp</del></<del style="color: red; font-weight: bold; text-decoration: none;">a</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">En un triángulo el ángulo </ins><<ins style="color: red; font-weight: bold; text-decoration: none;">math>ACB</ins>=<ins style="color: red; font-weight: bold; text-decoration: none;">90^\circ<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math>, el lado <math>AB \ <</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> y la suma de los lados <math>a+b<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>> <ins style="color: red; font-weight: bold; text-decoration: none;">son segmentos dados. Construir el triángulo <math>ABC</ins></<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>><ins style="color: red; font-weight: bold; text-decoration: none;">.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">lhJ5Xq </del>, <del style="color: red; font-weight: bold; text-decoration: none;">[url</del>=<del style="color: red; font-weight: bold; text-decoration: none;">http:</del>//<del style="color: red; font-weight: bold; text-decoration: none;">yhqxqpjrhimr</del>.<del style="color: red; font-weight: bold; text-decoration: none;">com</del>/<del style="color: red; font-weight: bold; text-decoration: none;">]yhqxqpjrhimr[</del>/<del style="color: red; font-weight: bold; text-decoration: none;">url]</del>, [<del style="color: red; font-weight: bold; text-decoration: none;">link=http</del>://<del style="color: red; font-weight: bold; text-decoration: none;">aegluqtsclvt</del>.<del style="color: red; font-weight: bold; text-decoration: none;">com</del>/<del style="color: red; font-weight: bold; text-decoration: none;">]aegluqtsclvt[</del>/<del style="color: red; font-weight: bold; text-decoration: none;">link</del>], <del style="color: red; font-weight: bold; text-decoration: none;">http:</del>//<del style="color: red; font-weight: bold; text-decoration: none;">yweoqdnyoekp</del>.<del style="color: red; font-weight: bold; text-decoration: none;">com</del>/</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Dibujamos el perímetro del triángulo que es el segmento <math>A''A'= c+a+b</math></ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">pues <math>AB</ins>=<ins style="color: red; font-weight: bold; text-decoration: none;">c<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math>. Señalamos el punto <math>B</math>, pues <math>A''B=AB<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math></ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">El punto <math>A<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> estará en la circunferencia de centro <math>B<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> y radio <math>BA''</math>. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Dibujamos en <math>A'</math> el ángulo de <math>45^\circ=90^\circ / 2</math>. El lado del ángulo corta al arco de circunferencia en las dos posiciones del punto <math>A</math>. Dibujamos <math>ABC</math>. El otro resultado</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">rayado, es el mismo triángulo colocado con los catetos en distinta dirección.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[<ins style="color: red; font-weight: bold; text-decoration: none;">[Imagen</ins>:<ins style="color: red; font-weight: bold; text-decoration: none;">DibujoTecnico_I-2_34.gif]]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema III==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos el lado <math>AB \ </math> de un triángulo y sus alturas <math>ha<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> y <math>hc<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math></ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Construir el triángulo <math>ABC<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Dibujamos el lado <math>AB \ <</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> y una recta paralela a <math>AB \ </math> a la distancia <math>hc</math>. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Trazamos un arco con radio <math>ha</math> y centro en <math>A</math> y la tangente desde <math>B</math> a dicho arco. El punto <math>C</math> será la intersección de la paralela con la tangente.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Hay otra solución simétrica a <math>ABC</math> respecto de <math>AB \ </math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_35.gif</ins>]<ins style="color: red; font-weight: bold; text-decoration: none;">]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema IV==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos el lado <math>AB \ </math> de un triángulo</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">un vértice <math>M<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> de su órtico y sabemos que el circuncentro <math>C<</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> dista una magnitud dada, <math>CP</math>, de <math>AB \ </math></ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Construir el triángulo.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Hallamos la mediatriz de <math>AB \ <</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">math> y situamos el circuncentro sobre ella. Dibujamos la circunferencia circunscrita, donde estará el vértice <math>C</math> buscado. Como <math>M</math> es un vértice del '''órtico''', es el pie de la altura sobre <math>AB \ </math>. Trazamos una perpendicular por <math>M</math> y hallamos <math>C</math> en su intersección con la circunscrita. Existe otra solución simétrica respecto de <math>AB \ </math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_36.gif]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema V==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema V==</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 31:</td>
<td colspan="2" class="diff-lineno">Línea 55:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_37.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_37.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Information is power and now I</del>'<del style="color: red; font-weight: bold; text-decoration: none;">m </del>a <del style="color: red; font-weight: bold; text-decoration: none;">!@#$ing diacttor</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema VI==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos un punto <math>P</math> de la circunferencia circunscrita al triángulo <math>ABC</math>, su recta de </ins>'<ins style="color: red; font-weight: bold; text-decoration: none;">''Simson''' <math>s</math> y las perpendiculares desde <math>P</math> la los lados del triángulo. Dibujar <math>ABC</math> y su circunferencia de '''Feuerbach'''. Comprobar que si <math>O \ </math> es el ortocentro, el punto medio de <math>PO</math> está sobre s y sobre dicha circunferencia.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Trazamos por <math>X, Y</math> y <math>Z</math> las perpendiculares </ins>a <ins style="color: red; font-weight: bold; text-decoration: none;"><math>PX, PY</math> y <math>PZ</math> respectivamente, que son las tres rectas que determinan el triángulo <math>ABC</math>. Hallamos su ortocentro <math>O \ </math> y su circunferencia de '''Feuerbach''' y comprobamos la posición del punto <math>M</math> como nos indica el enunciado. Podemos también comprobar que <math>P</math> está en la circunscrita de <math>ABC</math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_38</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">gif]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema VII==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema VII==</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 45:</td>
<td colspan="2" class="diff-lineno">Línea 75:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_39.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_39.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Articles like this really gasree the shafts of knowledge</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema VIII==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos el circuncentro, un vértice <math>A</math> la recta <math>na</math> que contiene a la mediana que pasa por <math>A</math> y la mediatriz <math>ma</math></ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Construir el triángulo <math>ABC</math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Dibujamos la circunscrita con centro en <math>C</math> y radio <math>CA</math>. Por el punto de intersección de <math>na</math> con <math>ma</math> trazamos la perpendicular a <math>ma</math>, obteniendo los vértices <math>B</math> y <math>C</math> de la solución.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_40.gif]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IX==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IX==</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 57:</td>
<td colspan="2" class="diff-lineno">Línea 93:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_41.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_41.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">I was srieuosly at DefCon 5 until I saw this post</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema X==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos la mediatriz <math>m_{AB}</math> , la bisectriz <math>b_C</math> y un punto <math>A</math> del triángulo <math>ABC</math></ins>. <ins style="color: red; font-weight: bold; text-decoration: none;"> Construir dicho triángulo.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">La intersección de la mediatriz y la bisectriz dadas es un punto <math>P</math> que pertenece a la circunscrita de <math>ABC</math>. Trazamos la mediatriz de <math>AP</math> y hallamos el centro de dicha circunscrita, que dibujamos. El punto <math>B</math> es el simétrico de <math>A</math> respecto de <math>m_{AB}</math> y el punto <math>C</math> la intersección de <math>b_C</math> con la circunscrita. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Dibujamos <math>ABC</math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_42.gif]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XI==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XI==</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 67:</td>
<td colspan="2" class="diff-lineno">Línea 111:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_43.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_43.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Gosh</del>, <del style="color: red; font-weight: bold; text-decoration: none;">I wish I would have had that ionfmratoin earlier!</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Problema XII==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Conocemos dos circunferencias</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">la menor inscrita y la mayor exinscrita a un triángulo <math>ABC</math>. Construir el triángulo.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Trazamos las rectas tangentes comunes interiores y exteriores a las circunferencias dadas. Los triángulos solución, simétricos respecto de la recta que une los centros de las circunferencias, son <math>ABC</math> y <math>A'B'C'</math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_44.gif]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XIII==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XIII==</div></td></tr>
</table>
EduardoRamos
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24403&oldid=prev
188.219.204.195: /* Problema XII */
2011-09-20T02:20:15Z
<p><span class="autocomment">Problema XII</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 02:20 20 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 67:</td>
<td colspan="2" class="diff-lineno">Línea 67:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_43.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_43.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema XII==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Gosh</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">I wish I would have had that ionfmratoin earlier!</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos dos circunferencias</del>, <del style="color: red; font-weight: bold; text-decoration: none;">la menor inscrita y la mayor exinscrita a un triángulo <math>ABC</math>. Construir el triángulo.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Trazamos las rectas tangentes comunes interiores y exteriores a las circunferencias dadas. Los triángulos solución, simétricos respecto de la recta que une los centros de las circunferencias, son <math>ABC</math> y <math>A'B'C'</math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_44.gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XIII==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XIII==</div></td></tr>
</table>
188.219.204.195
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24392&oldid=prev
84.237.79.18: /* Problema VI */
2011-09-20T01:25:02Z
<p><span class="autocomment">Problema VI</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 01:25 20 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 31:</td>
<td colspan="2" class="diff-lineno">Línea 31:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_37.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_37.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema VI==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Information is power and now I</ins>'<ins style="color: red; font-weight: bold; text-decoration: none;">m </ins>a <ins style="color: red; font-weight: bold; text-decoration: none;">!@#$ing diacttor</ins>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos un punto <math>P</math> de la circunferencia circunscrita al triángulo <math>ABC</math>, su recta de </del>'<del style="color: red; font-weight: bold; text-decoration: none;">''Simson''' <math>s</math> y las perpendiculares desde <math>P</math> la los lados del triángulo. Dibujar <math>ABC</math> y su circunferencia de '''Feuerbach'''. Comprobar que si <math>O \ </math> es el ortocentro, el punto medio de <math>PO</math> está sobre s y sobre dicha circunferencia.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Trazamos por <math>X, Y</math> y <math>Z</math> las perpendiculares </del>a <del style="color: red; font-weight: bold; text-decoration: none;"><math>PX, PY</math> y <math>PZ</math> respectivamente, que son las tres rectas que determinan el triángulo <math>ABC</math>. Hallamos su ortocentro <math>O \ </math> y su circunferencia de '''Feuerbach''' y comprobamos la posición del punto <math>M</math> como nos indica el enunciado. Podemos también comprobar que <math>P</math> está en la circunscrita de <math>ABC</math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_38</del>.<del style="color: red; font-weight: bold; text-decoration: none;">gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema VII==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema VII==</div></td></tr>
</table>
84.237.79.18
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24348&oldid=prev
86.62.117.211: /* Problema IV */
2011-09-19T10:38:36Z
<p><span class="autocomment">Problema IV</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 10:38 19 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 19:</td>
<td colspan="2" class="diff-lineno">Línea 19:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>OQZryW <a href="http://zebbeirbggfp.com/">zebbeirbggfp</a></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>OQZryW <a href="http://zebbeirbggfp.com/">zebbeirbggfp</a></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=<del style="color: red; font-weight: bold; text-decoration: none;">=Problema IV==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">lhJ5Xq , [url</ins>=<ins style="color: red; font-weight: bold; text-decoration: none;">http:</ins>//<ins style="color: red; font-weight: bold; text-decoration: none;">yhqxqpjrhimr.com</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">]yhqxqpjrhimr[</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">url]</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">[link=http:</ins>//<ins style="color: red; font-weight: bold; text-decoration: none;">aegluqtsclvt</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">com</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">]aegluqtsclvt[</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">link]</ins>, <ins style="color: red; font-weight: bold; text-decoration: none;">http:</ins>//<ins style="color: red; font-weight: bold; text-decoration: none;">yweoqdnyoekp</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">com</ins>/</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos el lado <math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> de un triángulo, un vértice <math>M<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> de su órtico y sabemos que el circuncentro <math>C<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> dista una magnitud dada, <math>CP<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math></del>, <del style="color: red; font-weight: bold; text-decoration: none;">de <math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math>. Construir el triángulo.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Hallamos la mediatriz de <math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> y situamos el circuncentro sobre ella</del>. <del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos la circunferencia circunscrita, donde estará el vértice <math>C<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> buscado. Como <math>M<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> es un vértice del '''órtico'''</del>, <del style="color: red; font-weight: bold; text-decoration: none;">es el pie de la altura sobre <math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math>. Trazamos una perpendicular por <math>M<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> y hallamos <math>C</math> en su intersección con la circunscrita</del>. <del style="color: red; font-weight: bold; text-decoration: none;">Existe otra solución simétrica respecto de <math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_36.gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema V==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema V==</div></td></tr>
</table>
86.62.117.211
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24249&oldid=prev
193.189.115.93: /* Problema VIII */
2011-09-18T18:08:00Z
<p><span class="autocomment">Problema VIII</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 18:08 18 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 57:</td>
<td colspan="2" class="diff-lineno">Línea 57:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_39.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_39.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema VIII==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Articles like this really gasree the shafts of knowledge</ins>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos el circuncentro, un vértice <math>A</math> la recta <math>na</math> que contiene a la mediana que pasa por <math>A</math> y la mediatriz <math>ma</math></del>. <del style="color: red; font-weight: bold; text-decoration: none;">Construir el triángulo <math>ABC</math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos la circunscrita con centro en <math>C</math> y radio <math>CA</math>. Por el punto de intersección de <math>na</math> con <math>ma</math> trazamos la perpendicular a <math>ma</math>, obteniendo los vértices <math>B</math> y <math>C</math> de la solución.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_40.gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IX==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IX==</div></td></tr>
</table>
193.189.115.93
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24220&oldid=prev
91.121.195.17: /* Problema X */
2011-09-18T11:55:07Z
<p><span class="autocomment">Problema X</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 11:55 18 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 75:</td>
<td colspan="2" class="diff-lineno">Línea 75:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_41.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_41.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema X==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">I was srieuosly at DefCon 5 until I saw this post</ins>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos la mediatriz <math>m_{AB}</math> , la bisectriz <math>b_C</math> y un punto <math>A</math> del triángulo <math>ABC</math></del>. <del style="color: red; font-weight: bold; text-decoration: none;"> Construir dicho triángulo.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">La intersección de la mediatriz y la bisectriz dadas es un punto <math>P</math> que pertenece a la circunscrita de <math>ABC</math>. Trazamos la mediatriz de <math>AP</math> y hallamos el centro de dicha circunscrita, que dibujamos. El punto <math>B</math> es el simétrico de <math>A</math> respecto de <math>m_{AB}</math> y el punto <math>C</math> la intersección de <math>b_C</math> con la circunscrita. </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos <math>ABC</math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_42.gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XI==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema XI==</div></td></tr>
</table>
91.121.195.17
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24209&oldid=prev
217.72.91.180: /* Problema III */
2011-09-18T08:04:04Z
<p><span class="autocomment">Problema III</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 08:04 18 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 17:</td>
<td colspan="2" class="diff-lineno">Línea 17:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Hey, subtle must be your mildde name. Great post!</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Hey, subtle must be your mildde name. Great post!</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema III==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">OQZryW </ins><a <ins style="color: red; font-weight: bold; text-decoration: none;">href="http:</ins>//<ins style="color: red; font-weight: bold; text-decoration: none;">zebbeirbggfp</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">com</ins>/<ins style="color: red; font-weight: bold; text-decoration: none;">"</ins>><ins style="color: red; font-weight: bold; text-decoration: none;">zebbeirbggfp</ins></a></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Conocemos el lado </del><<del style="color: red; font-weight: bold; text-decoration: none;">math>AB \ </math> de un triángulo y sus alturas <math>ha</math> y <math>hc</math>. Construir el triángulo <math>ABC</math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos el lado <math>AB \ </math> y una recta paralela </del>a <del style="color: red; font-weight: bold; text-decoration: none;"><math>AB \ <</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math> a la distancia <math>hc<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math></del>. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Trazamos un arco con radio <math>ha<</del>/<del style="color: red; font-weight: bold; text-decoration: none;">math</del>> <del style="color: red; font-weight: bold; text-decoration: none;">y centro en <math>A</del></<del style="color: red; font-weight: bold; text-decoration: none;">math> y la tangente desde <math>B</math> </del>a <del style="color: red; font-weight: bold; text-decoration: none;">dicho arco. El punto <math</del>><del style="color: red; font-weight: bold; text-decoration: none;">C</math> será la intersección de la paralela con la tangente.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Hay otra solución simétrica a <math>ABC</math> respecto de <math>AB \ </math>.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_35.gif]]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IV==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema IV==</div></td></tr>
</table>
217.72.91.180
http://wikillerato.org/index.php?title=Algunos_problemas_con_tri%C3%A1ngulos&diff=24169&oldid=prev
190.9.128.96: /* Problema II */
2011-09-17T23:55:34Z
<p><span class="autocomment">Problema II</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 23:55 17 sep 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 15:</td>
<td colspan="2" class="diff-lineno">Línea 15:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Imagen:DibujoTecnico_I-2_33.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">==Problema II==</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Hey, subtle must be your mildde name. Great post!</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">En un triángulo el ángulo <math>ACB=90^\circ</math>, el lado <math>AB \ </math> y la suma de los lados <math>a+b</math> son segmentos dados. Construir el triángulo <math>ABC</math>.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos el perímetro del triángulo que es el segmento <math>A''A'= c+a+b</math>, pues <math>AB=c</math>. Señalamos el punto <math>B</math>, pues <math>A''B=AB</math>. El punto <math>A</math> estará en la circunferencia de centro <math>B</math> y radio <math>BA''</math>. </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Dibujamos en <math>A'</math> el ángulo de <math>45^\circ=90^\circ / 2</math>. El lado del ángulo corta al arco de circunferencia en las dos posiciones del punto <math>A</math>. Dibujamos <math>ABC</math>. El otro resultado, rayado, es el mismo triángulo colocado con los catetos en distinta dirección.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Imagen:DibujoTecnico_I-2_34.gif]]</del></div></td><td colspan="2"> </td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema III==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Problema III==</div></td></tr>
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