{"id":3559,"date":"2025-03-23T10:58:39","date_gmt":"2025-03-23T10:58:39","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3559"},"modified":"2025-04-16T07:17:33","modified_gmt":"2025-04-16T07:17:33","slug":"propiedad-del-ortocentro","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2025\/03\/23\/propiedad-del-ortocentro\/","title":{"rendered":"Propiedad del ortocentro"},"content":{"rendered":"<pre>Problema 9 de la Fase Local de la Olimpiada Matem\u00e1tica Espa\u00f1ola (2025)\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n\n\n<p>Sea ABC un tri\u00e1ngulo acut\u00e1ngulo cuyos lados tienen longitudes a, b y c, y sea S el \u00e1rea del tri\u00e1ngulo.<\/p>\n\n\n\n<p>Sea P un punto interior del tri\u00e1ngulo de forma que a\u00b7|PA| + b\u00b7|PB| + c\u00b7|PC| = 4S.<\/p>\n\n\n\n<p>Demuestra que P es el ortocentro del tri\u00e1ngulo ABC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2025\/03\/379.Ortocentro.png\" alt=\"\" class=\"wp-image-3560\" \/><\/figure>\n\n\n\n<p>Soluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2025\/04\/12\/solucion-a-propiedad-del-ortocentro\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 9 de la Fase Local de la Olimpiada Matem\u00e1tica Espa\u00f1ola (2025) Se dirige a una edad de: 16-17 a\u00f1os Sea ABC un tri\u00e1ngulo acut\u00e1ngulo cuyos lados tienen longitudes a, b y c, y sea S el \u00e1rea del tri\u00e1ngulo. Sea P un punto interior del tri\u00e1ngulo de forma que a\u00b7|PA| + b\u00b7|PB| + c\u00b7|PC| [&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-3559","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\/3559","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=3559"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3559\/revisions"}],"predecessor-version":[{"id":3579,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3559\/revisions\/3579"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}