{"id":1589,"date":"2016-08-17T01:00:16","date_gmt":"2016-08-17T00:00:16","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=1589"},"modified":"2018-02-17T02:05:53","modified_gmt":"2018-02-17T01:05:53","slug":"devoir-maison-n4","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/devoir-maison-n4\/","title":{"rendered":"Encercl\u00e9"},"content":{"rendered":"<p>Sur la figure ci-dessous, les trois cercles c<sub>1<\/sub>, c<sub>2<\/sub> et c<sub>3<\/sub> de centres respectifs I, O et J, ont le m\u00eame rayon, qui est un entier naturel <em>x<\/em>.\u00a0 La droite (NM) est tangente au cercle c<sub>3<\/sub> en M et coupe c<sub>2<\/sub> en A et B.<img loading=\"lazy\" decoding=\"async\" class=\" wp-image-1588 aligncenter\" src=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/dm_04-300x115.png\" alt=\"dm_04\" width=\"394\" height=\"151\" srcset=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/dm_04-300x115.png 300w, https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/08\/dm_04.png 533w\" sizes=\"auto, (max-width: 394px) 100vw, 394px\" \/><\/p>\n<p>On pose OH = <em>a<\/em>\u00a0 et\u00a0 AB = <em>b<\/em>.<\/p>\n<p><strong>\u00a01)\u00a0\u00a0 Calcul de <em>a<\/em><\/strong><\/p>\n<p><strong>a. <\/strong>A l\u2019aide du th\u00e9or\u00e8me de Thal\u00e8s, exprimer a en fonction de <em>x<\/em>.<\/p>\n<p><strong>b. <\/strong>Quelle est la nature du nombre <em>a<\/em>?<\/p>\n<p><strong>c. <\/strong>Quelles sont les valeurs de <em>x<\/em> pour lesquelles <em>a<\/em> est un nombre entier\u00a0?<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>2)\u00a0\u00a0 Calcul de <em>b<\/em><\/strong><\/p>\n<p><strong>a. <\/strong>A l\u2019aide du th\u00e9or\u00e8me de Pythagore, exprimer HB, puis <em>b<\/em> en fonction de <em>x<\/em>.<\/p>\n<p><strong>b. <\/strong>Quelle est la nature du nombre <em>b <\/em>?<\/p>\n<p><strong>c. <\/strong>Quelles sont les valeurs de <em>x<\/em> pour lesquelles <em>b<\/em> est un entier\u00a0?<\/p>\n<p><strong>3)<\/strong>\u00a0\u00a0 R\u00e9aliser la figure pour <em>x<\/em> = 5 cm.<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/Encercl\u00e9.docx\">Fiche \u00e9l\u00e8ve Encercl\u00e9 word<\/a><\/p>\n<p><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2017\/06\/Encercl\u00e9.pdf\">Fiche \u00e9l\u00e8ve Encercl\u00e9 pdf<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sur la figure ci-dessous, les trois cercles c1, c2 et c3 de centres respectifs I, O et J, ont le m\u00eame rayon, qui est un entier naturel x.\u00a0 La droite (NM) est tangente au cercle c3 en M et coupe c2 en A et B. On pose OH = a\u00a0 et\u00a0 AB = b. \u00a01)\u00a0\u00a0 &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/devoir-maison-n4\/\">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":[23,22],"tags":[],"class_list":["post-1589","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1589","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=1589"}],"version-history":[{"count":9,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1589\/revisions"}],"predecessor-version":[{"id":2795,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/1589\/revisions\/2795"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=1589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=1589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=1589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}