{"id":13475,"date":"2018-02-04T21:25:00","date_gmt":"2018-02-04T21:25:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13475"},"modified":"2022-01-17T16:32:24","modified_gmt":"2022-01-17T16:32:24","slug":"na-figura-esta-representada-uma-circunferencia-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13475","title":{"rendered":"Na figura est\u00e1 representada uma circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13475' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13475' class='GTTabs_curr'><a  id=\"13475_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13475' ><a  id=\"13475_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_13475'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13476\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13476\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\" data-orig-size=\"225,255\" 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\/02\/9V1Pag152-3.png\" class=\"alignright size-full wp-image-13476\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\" alt=\"\" width=\"225\" height=\"255\" \/><\/a>Na figura est\u00e1 representada uma circunfer\u00eancia de centro no ponto O.<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>Os pontos A, B, C, D e E pertencem \u00e0 circunfer\u00eancia;<\/li>\n<li>[AD] \u00e9 um di\u00e2metro da circunfer\u00eancia;<\/li>\n<li>O ponto P \u00e9 o ponto de interse\u00e7\u00e3o dos segmentos de reta [AC] e [BD];<\/li>\n<li>\\(C\\widehat AD = 40^\\circ \\).<\/li>\n<\/ul>\n<ol>\n<li>Qual das afirma\u00e7\u00f5es seguintes \u00e9 verdadeira?<br \/>\n[A] O ponto O pertence \u00e0 mediatriz do segmento de reta [AP].<br \/>\n[B] O ponto O pertence \u00e0 mediatriz do segmento de reta [BC].<br \/>\n[C] O ponto B pertence \u00e0 mediatriz do segmento de reta [BC].<br \/>\n[D] O ponto B pertence \u00e0 mediatriz do segmento de reta [AP].<\/li>\n<li>Qual \u00e9 a amplitude, em graus, do arco AC?<br \/>\nMostra como chegaste \u00e0 resposta.<\/li>\n<li>Relativamente ao tri\u00e2ngulo ret\u00e2ngulo [AED], admite que:\u00a0\\(\\overline {AE} = 6,8\\) cm e\u00a0\\(\\overline {DE} = 3,2\\) cm.<br \/>\nDetermina o per\u00edmetro do c\u00edrculo.<br \/>\nApresenta o resultado em cent\u00edmetros, arredondado \u00e0s d\u00e9cimas.<br \/>\nApresenta os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13475' onClick='GTTabs_show(1,13475)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13475'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ul>\n<li>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13476\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13476\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\" data-orig-size=\"225,255\" 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\/02\/9V1Pag152-3.png\" class=\"alignright size-full wp-image-13476\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3.png\" alt=\"\" width=\"225\" height=\"255\" \/><\/a>Os pontos A, B, C, D e E pertencem \u00e0 circunfer\u00eancia;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>[AD] \u00e9 um di\u00e2metro da circunfer\u00eancia;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>O ponto P \u00e9 o ponto de interse\u00e7\u00e3o dos segmentos de reta [AC] e [BD];<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>\\(C\\widehat AD = 40^\\circ \\).<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<ol>\n<li>A afirma\u00e7\u00e3o verdadeira \u00e9 a <strong>B<\/strong>, pois o ponto O \u00e9 equidistante dos pontos B e C.<br \/>\n\u00ad<\/li>\n<li>\\(\\overparen{AC} = \\overparen{AD} &#8211; \\overparen{CD} = 180^\\circ &#8211; 2 \\times C\\widehat AD = 180^\\circ &#8211; 2 \\times 40^\\circ = 100^\\circ \\).<br \/>\n\u00ad<\/li>\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [AED], vem: \\(\\overline {AD} = \\sqrt {{{\\overline {AE} }^2} + {{\\overline {ED} }^2}} = \\sqrt {{{6,8}^2} + {{3,2}^2}} = \\sqrt {56,48} \\) cm.<br \/>\nLogo, o per\u00edmetro do c\u00edrculo \u00e9 \\({P_\\bigcirc } = \\pi \\times \\overline {AD} = \\pi \\times \\sqrt {56,48} \\approx 23,6\\) cm.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13475' onClick='GTTabs_show(0,13475)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura est\u00e1 representada uma circunfer\u00eancia de centro no ponto O. Sabe-se que: Os pontos A, B, C, D e E pertencem \u00e0 circunfer\u00eancia; [AD] \u00e9 um di\u00e2metro da circunfer\u00eancia; O&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20508,"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-13475","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":4238,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag152-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13475","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=13475"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13475\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20508"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13475"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}