{"id":1485,"date":"2016-08-16T21:31:36","date_gmt":"2016-08-16T20:31:36","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1485"},"modified":"2018-02-17T02:06:17","modified_gmt":"2018-02-17T01:06:17","slug":"configurations-et-symetrie-axiale","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/configurations-et-symetrie-axiale\/","title":{"rendered":"Configurations et sym\u00e9trie axiale"},"content":{"rendered":"<p>Sur la figure ci-contre,<img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1492 alignright\" src=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/configuration-et-sym\u00e9trie-axiale-300x202.png\" alt=\"configuration et sym\u00e9trie axiale\" width=\"300\" height=\"202\" srcset=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/configuration-et-sym\u00e9trie-axiale-300x202.png 300w, https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/configuration-et-sym\u00e9trie-axiale-768x516.png 768w, https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/configuration-et-sym\u00e9trie-axiale.png 821w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>ABC est un triangle quelconque inscrit dans le cercle\u00a0\u0393 de centre O tel que :<\/p>\n<ul>\n<li>la tangente en A au cercle \u0393 coupe la droite (BC) en F ;<\/li>\n<li>le point E diam\u00e9tralement oppos\u00e9 au point A sur le cercle \u0393 est distinct de B et C\u00a0;<\/li>\n<li>les points I et J sont les milieux respectifs des segments [AB] et [AC].<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ol>\n<li>Citer les triangles isoc\u00e8les que l\u2019on peut former \u00e0 l\u2019aide des points de la figure.<\/li>\n<\/ol>\n<ol start=\"2\">\n<li>Justifier que les triangles FAO et AIO sont rectangles.<\/li>\n<\/ol>\n<ol start=\"3\">\n<li>La droite (OI) coupe la droite (AF) en G.<\/li>\n<\/ol>\n<p>On consid\u00e8re la sym\u00e9trie <strong>s<\/strong> d\u2019axe (OI). Compl\u00e9ter le tableau :<\/p>\n<table width=\"204\">\n<tbody>\n<tr>\n<td width=\"102\"><\/td>\n<td width=\"102\">image par <strong>s<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"102\">A<\/td>\n<td width=\"102\"><\/td>\n<\/tr>\n<tr>\n<td width=\"102\">O<\/td>\n<td width=\"102\"><\/td>\n<\/tr>\n<tr>\n<td width=\"102\">G<\/td>\n<td width=\"102\"><\/td>\n<\/tr>\n<tr>\n<td width=\"102\">(AO)<\/td>\n<td width=\"102\"><\/td>\n<\/tr>\n<tr>\n<td width=\"102\">(AG)<\/td>\n<td width=\"102\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Montrer que la droite (BG) est tangente au cercle \u0393.<\/p>\n<p>&nbsp;<\/p>\n<p>Des points qui appartiennent \u00e0 un m\u00eame cercle sont dits cocycliques. Justifier que les points A, I, O et J sont cocycliques.<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/utiliser_configuration_symetrie_axiale.docx\">Fiche \u00e9l\u00e8ve Configurations et sym\u00e9trie axiale word<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/utiliser_configuration_symetrie_axiale.pdf\">Fiche \u00e9l\u00e8ve Configurations et sym\u00e9trie axiale pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sur la figure ci-contre, ABC est un triangle quelconque inscrit dans le cercle\u00a0\u0393 de centre O tel que : la tangente en A au cercle \u0393 coupe la droite (BC) en F ; le point E diam\u00e9tralement oppos\u00e9 au point A sur le cercle \u0393 est distinct de B et C\u00a0; les points I et &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/configurations-et-symetrie-axiale\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23],"tags":[],"class_list":["post-1485","post","type-post","status-publish","format-standard","hentry","category-seconde","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=1485"}],"version-history":[{"count":8,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1485\/revisions"}],"predecessor-version":[{"id":2779,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1485\/revisions\/2779"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}