{"id":13245,"date":"2018-01-11T16:26:30","date_gmt":"2018-01-11T16:26:30","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13245"},"modified":"2022-01-16T23:23:00","modified_gmt":"2022-01-16T23:23:00","slug":"13245","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13245","title":{"rendered":"Considera a circunfer\u00eancia de centro O"},"content":{"rendered":"<p><ul id='GTTabs_ul_13245' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13245' class='GTTabs_curr'><a  id=\"13245_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13245' ><a  id=\"13245_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_13245'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13246\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13246\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2.png\" data-orig-size=\"235,210\" 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\/9V1Pag129-2.png\" class=\"alignright size-full wp-image-13246\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2.png\" alt=\"\" width=\"235\" height=\"210\" \/><\/a>Considera a circunfer\u00eancia de centro O.<\/p>\n<ol>\n<li>[AB] e [DC] s\u00e3o di\u00e2metros. Porqu\u00ea?<\/li>\n<li>Se \\(A\\widehat OD = 34^\\circ \\), calcula:<\/li>\n<\/ol>\n<ul>\n<li>\\(C\\widehat OB\\)<\/li>\n<li>\\(A\\widehat BD\\)<\/li>\n<li>\\(\\overparen{DB}\\)<\/li>\n<li>\\(B\\widehat AD\\)<\/li>\n<li>\\(A\\widehat DB\\)<\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13245' onClick='GTTabs_show(1,13245)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13245'>\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\/9V1Pag129-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13246\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13246\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2.png\" data-orig-size=\"235,210\" 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\/9V1Pag129-2.png\" class=\"alignright size-full wp-image-13246\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2.png\" alt=\"\" width=\"235\" height=\"210\" \/><\/a>[AB] e [DC] s\u00e3o di\u00e2metros, pois s\u00e3o cordas que cont\u00eam o centro da circunfer\u00eancia.<\/li>\n<li>Se \\(A\\widehat OD = 34^\\circ \\), calcula:<\/li>\n<\/ol>\n<ul>\n<li>\\(C\\widehat OB = A\\widehat OD = 34^\\circ \\), pois os \u00e2ngulos BOC e AOD s\u00e3o verticalmente opostos.<\/li>\n<li>\\(A\\widehat BD = \\frac{{\\overparen{AD}}}{2} = \\frac{{A\\widehat OD}}{2} = \\frac{{34^\\circ }}{2} = 17^\\circ \\)<\/li>\n<li>\\(\\overparen{DB} = \\overparen{AB} &#8211; \\overparen{AD} = 180^\\circ &#8211; 34^\\circ = 146^\\circ \\)<\/li>\n<li>\\(B\\widehat AD = \\frac{{\\overparen{DB}}}{2} = \\frac{{146^\\circ }}{2} = 73^\\circ \\)<\/li>\n<li>\\(A\\widehat DB = \\frac{{\\overparen{AB}}}{2} = \\frac{{180^\\circ }}{2} = 90^\\circ \\)<\/li>\n<\/ul>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13245' onClick='GTTabs_show(0,13245)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a circunfer\u00eancia de centro O. [AB] e [DC] s\u00e3o di\u00e2metros. Porqu\u00ea? Se \\(A\\widehat OD = 34^\\circ \\), calcula: \\(C\\widehat OB\\) \\(A\\widehat BD\\) \\(\\overparen{DB}\\) \\(B\\widehat AD\\) \\(A\\widehat DB\\) Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20445,"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-13245","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":2363,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13245","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=13245"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13245\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20445"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13245"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}