{"id":3190,"date":"2024-02-17T09:41:58","date_gmt":"2024-02-17T09:41:58","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3190"},"modified":"2024-02-24T12:58:18","modified_gmt":"2024-02-24T12:58:18","slug":"perpendicular-en-un-cuadrilatero","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2024\/02\/17\/perpendicular-en-un-cuadrilatero\/","title":{"rendered":"Perpendicular en un cuadril\u00e1tero"},"content":{"rendered":"<pre>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2024 (viernes)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Sea ABCD un cuadril\u00e1tero.<\/p>\n<p>Sean J e I los puntos medios de las diagonales AC y BD, respectivamente.<\/p>\n<p>Sea G el punto de la recta BC tal que DG es perpendicular a BC y sea H el punto de la recta AD tal que CH es perpendicular a AD.<\/p>\n<p>Las rectas DG y CH se cortan en el punto K.<\/p>\n<p>Sea E el punto de la recta BC tal que AE es perpendicular a BC y sea F el punto de la recta AD tal que BF es perpendicular a AD.<\/p>\n<p>Las rectas AE y BF se cortan en el punto L.<\/p>\n<p>Probar que KL es perpendicular a JI.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2024\/02\/337.cuadri.png\" alt=\"\" width=\"300\" height=\"300\" class=\"alignnone size-full wp-image-3191\" \/><\/p>\n<p>Soluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2024\/02\/24\/solucion-a-perpendicular-en-un-cuadrilatero\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 3 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2024 (viernes) Se dirige a una edad de: 16-17 a\u00f1os Sea ABCD un cuadril\u00e1tero. Sean J e I los puntos medios de las diagonales AC y BD, respectivamente. Sea G el punto de la recta BC tal que DG es perpendicular a BC [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2242029,2849],"tags":[],"class_list":["post-3190","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-ome","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3190","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=3190"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3190\/revisions"}],"predecessor-version":[{"id":3199,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3190\/revisions\/3199"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}