{"id":13188,"date":"2018-01-08T23:07:20","date_gmt":"2018-01-08T23:07:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13188"},"modified":"2022-01-16T22:21:20","modified_gmt":"2022-01-16T22:21:20","slug":"sobre-uma-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13188","title":{"rendered":"Sobre uma circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13188' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13188' class='GTTabs_curr'><a  id=\"13188_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13188' ><a  id=\"13188_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_13188'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13192\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13192\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png\" data-orig-size=\"360,310\" 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\/circunf.png\" class=\"alignright size-medium wp-image-13192\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf-300x258.png\" alt=\"\" width=\"300\" height=\"258\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf-300x258.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png 360w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Na figura, [AD] \u00e9 um di\u00e2metro da circunfer\u00eancia de centro O,\u00a0\\(A\\widehat OB = 60^\\circ \\) e\u00a0\\(\\dot OC\\) \u00e9 a bissetriz do \u00e2ngulo BOD.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Calcula\u00a0\\(B\\widehat OC\\) e\u00a0\\(C\\widehat OD\\).<\/li>\n<li>O que podemos concluir em rela\u00e7\u00e3o a $\\newcommand{arc}[1]{\\stackrel{\\Large\\frown}{#1}}\\arc{AB}$,\u00a0$\\newcommand{arc}[1]{\\stackrel{\\Large\\frown}{#1}}\\arc{BC}$ e\u00a0$\\newcommand{arc}[1]{\\stackrel{\\Large\\frown}{#1}}\\arc{CD}$? Porqu\u00ea?<\/li>\n<li>E em rela\u00e7\u00e3o a\u00a0\\(\\overline {AB} \\),\u00a0\\(\\overline {BC} \\) e\u00a0\\(\\overline {CD} \\)? Porqu\u00ea?<\/li>\n<li>Supondo que \\(\\overline {AO} = 2\\) cm, calcula o comprimento do arco AC.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13188' onClick='GTTabs_show(1,13188)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13188'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13192\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13192\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png\" data-orig-size=\"360,310\" 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\/circunf.png\" class=\"alignright size-medium wp-image-13192\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf-300x258.png\" alt=\"\" width=\"300\" height=\"258\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf-300x258.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/circunf.png 360w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Ora, \\(B\\widehat OC = C\\widehat OD = \\frac{{B\\widehat OD}}{2} = \\frac{{A\\widehat OD &#8211; A\\widehat OB}}{2} = \\frac{{180^\\circ &#8211; 60^\\circ }}{2} = 60^\\circ \\).<br \/>\n\u00ad<\/li>\n<li>Os arcos AB, BC e CD t\u00eam iguais amplitudes (\\(60^\\circ \\)), pois, como vimos na al\u00ednea anterior, os respetivos \u00e2ngulos ao centro s\u00e3o geometricamente iguais.<br \/>\n\u00ad<\/li>\n<li>As cordas [AB], [BC] e [CD] t\u00eam iguais comprimentos, pois s\u00e3o correspondentes a arcos e a \u00e2ngulos ao centro geometricamente iguais.<br \/>\n\u00ad<\/li>\n<li>O arco AC tem\u00a0\\(l = \\frac{{120^\\circ }}{{360^\\circ }} \\times {P_\\bigcirc } = \\frac{1}{3} \\times 2\\pi \\times 2 = \\frac{{4\\pi }}{3}\\) cm de comprimento.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13188' onClick='GTTabs_show(0,13188)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, [AD] \u00e9 um di\u00e2metro da circunfer\u00eancia de centro O,\u00a0\\(A\\widehat OB = 60^\\circ \\) e\u00a0\\(\\dot OC\\) \u00e9 a bissetriz do \u00e2ngulo BOD. Calcula\u00a0\\(B\\widehat OC\\) e\u00a0\\(C\\widehat OD\\). O que podemos concluir&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20430,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,279,457,188],"series":[],"class_list":["post-13188","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-arco-de-circunferencia","tag-circunferencia"],"views":2468,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag119-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13188","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=13188"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13188\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20430"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13188"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13188"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13188"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}