{"id":750,"date":"2018-09-16T20:29:53","date_gmt":"2018-09-16T20:29:53","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=750"},"modified":"2018-09-30T07:30:53","modified_gmt":"2018-09-30T07:30:53","slug":"circunferencia-fija","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2018\/09\/16\/circunferencia-fija\/","title":{"rendered":"Circunferencia fija"},"content":{"rendered":"<pre>Problema 1 de la Olimpiada Matem\u00e1tica Femenina Europea (EGMO 2018)\r\nSe dirige a una edad de: 17 a\u00f1os<\/pre>\n<p>Sea ABC un tri\u00e1ngulo de forma que CA = CB y el \u00e1ngulo ACB mida 120\u00ba, y sea M el punto medio de AB.<\/p>\n<p>Sea P un punto variable de la circunferencia que pasa por A, B y C.<\/p>\n<p>Sea Q el punto en el segmento CP tal que QP = 2QC.<\/p>\n<p>Se sabe que la recta que pasa por P y es perpendicular a la recta AB interseca a la recta MQ en un \u00fanico punto N.<\/p>\n<p>Demuestre que existe una circunferencia fija tal que N se encuentra en esa circunferencia  para todas las posibles posiciones de P.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2018\/09\/60.Circunferenciafija.gif\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-753\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 1 de la Olimpiada Matem\u00e1tica Femenina Europea (EGMO 2018) Se dirige a una edad de: 17 a\u00f1os Sea ABC un tri\u00e1ngulo de forma que CA = CB y el \u00e1ngulo ACB mida 120\u00ba, y sea M el punto medio de AB. Sea P un punto variable de la circunferencia que pasa por A, B [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242015,1738,2849],"tags":[],"class_list":["post-750","post","type-post","status-publish","format-standard","hentry","category-egmo","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=750"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/750\/revisions"}],"predecessor-version":[{"id":755,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/750\/revisions\/755"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}