{"id":13265,"date":"2018-01-11T18:39:36","date_gmt":"2018-01-11T18:39:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13265"},"modified":"2022-01-16T23:39:14","modified_gmt":"2022-01-16T23:39:14","slug":"o-e-o-centro-da-circunfrencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13265","title":{"rendered":"O \u00e9 o centro da circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13265' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13265' class='GTTabs_curr'><a  id=\"13265_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13265' ><a  id=\"13265_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_13265'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13266\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13266\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" data-orig-size=\"225,230\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Circunfer\u00eancia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" class=\"alignright size-full wp-image-13266\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" alt=\"\" width=\"225\" height=\"230\" \/><\/a>Na figura, O \u00e9 o centro da circunfer\u00eancia e\u00a0\\(a = 28^\\circ \\).<\/p>\n<ol>\n<li>Classifica o tri\u00e2ngulo [ETO] quanto aos lados e quanto aos \u00e2ngulos.<\/li>\n<li>Calcula o valor de x, amplitude do \u00e2ngulo EQT.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13265' onClick='GTTabs_show(1,13265)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13265'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13266\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13266\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" data-orig-size=\"225,230\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Circunfer\u00eancia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" class=\"alignright size-full wp-image-13266\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6.png\" alt=\"\" width=\"225\" height=\"230\" \/><\/a>O tri\u00e2ngulo [ETO], quanto aos lados, \u00e9 is\u00f3sceles e, quanto aos \u00e2ngulos, \u00e9 obtus\u00e2ngulo.<br \/>\nCom efeito, os lados [EO] e [OT] s\u00e3o segmentos de reta geometricamente iguais, pois s\u00e3o raios da mesma circunfer\u00eancia.<br \/>\nComo, num tri\u00e2ngulo, a lados iguais op\u00f5em-se \u00e2ngulos iguais, ent\u00e3o \\(b = 28^\\circ \\); consequentemente, \\(E\\widehat OT = 180^\\circ &#8211; (28^\\circ + 28^\\circ ) = 124^\\circ \\), pois a soma das amplitudes dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 igual a 360 graus.<br \/>\n\u00ad<\/li>\n<li>Ora, \\(x = E\\widehat QT = \\frac{{\\overparen{ET}}}{2} = \\frac{{E\\widehat OT}}{2} = \\frac{{124^\\circ }}{2} = 62^\\circ \\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13265' onClick='GTTabs_show(0,13265)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, O \u00e9 o centro da circunfer\u00eancia e\u00a0\\(a = 28^\\circ \\). Classifica o tri\u00e2ngulo [ETO] quanto aos lados e quanto aos \u00e2ngulos. Calcula o valor de x, amplitude do \u00e2ngulo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20451,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,279,280,188],"series":[],"class_list":["post-13265","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-9-o-ano","tag-angulo-ao-centro","tag-angulo-inscrito","tag-circunferencia"],"views":2810,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13265","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=13265"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13265\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20451"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13265"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13265"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13265"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}