{"id":2101,"date":"2021-07-04T07:37:59","date_gmt":"2021-07-04T07:37:59","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2101"},"modified":"2021-07-11T17:02:25","modified_gmt":"2021-07-11T17:02:25","slug":"angulo-en-esfera","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2021\/07\/04\/angulo-en-esfera\/","title":{"rendered":"\u00c1ngulo en esfera"},"content":{"rendered":"<pre>Problema 1 de la fase nacional de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2021)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Los v\u00e9rtices A, B y C  de un tri\u00e1ngulo equil\u00e1tero de lado 1 est\u00e1n en la superficie de una esfera de radio 1 y centro O.<\/p>\n<p>Sea D la proyecci\u00f3n ortogonal de A sobre el plano \u03b1, determinado por B, C y O.<\/p>\n<p>Llamamos N a uno de los cortes con la esfera de la recta perpendicular a \u03b1 por O.<\/p>\n<p>Halla la medida del \u00e1ngulo DNO.<\/p>\n<p>(Nota: la proyecci\u00f3n ortogonal de A sobre el plano \u03b1 es el punto de corte con \u03b1 de la recta que pasa por A y es perpendicular a \u03b1.)<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/203.Anguloenesfera.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-2104\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/203.Anguloenesfera.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/203.Anguloenesfera-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2021\/07\/10\/solucion-a-angulo-en-esfera\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 1 de la fase nacional de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2021) Se dirige a una edad de: 16-17 a\u00f1os Los v\u00e9rtices A, B y C de un tri\u00e1ngulo equil\u00e1tero de lado 1 est\u00e1n en la superficie de una esfera de radio 1 y centro O. Sea D la proyecci\u00f3n ortogonal de A sobre [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2849],"tags":[],"class_list":["post-2101","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2101","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=2101"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2101\/revisions"}],"predecessor-version":[{"id":2112,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2101\/revisions\/2112"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}