{"id":13272,"date":"2018-01-11T21:12:53","date_gmt":"2018-01-11T21:12:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13272"},"modified":"2022-01-16T23:46:09","modified_gmt":"2022-01-16T23:46:09","slug":"quatro-pontos-de-uma-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13272","title":{"rendered":"Quatro pontos de uma circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13272' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13272' class='GTTabs_curr'><a  id=\"13272_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13272' ><a  id=\"13272_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_13272'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13274\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13274\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\" data-orig-size=\"235,220\" 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\/9V1Pag129-8.png\" class=\"alignright size-full wp-image-13274\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\" alt=\"\" width=\"235\" height=\"220\" \/><\/a>Na figura, est\u00e1 representada uma circunfer\u00eancia de centro O e nela quatro pontos A, B, C e D, tais que \\(\\overline {AB} = \\overline {CD} \\).<\/p>\n<ol>\n<li>Justifica que \\(\\overline {BD} = \\overline {AC} \\).<\/li>\n<li>Supondo que a amplitude do arco maior BC mede 185\u00ba (o arco menor BC \u00e9 o arco BAC) e que a do arco AD mede 80\u00ba, determina a medida da amplitude do \u00e2ngulo CAD.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13272' onClick='GTTabs_show(1,13272)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13272'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13274\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13274\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\" data-orig-size=\"235,220\" 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\/9V1Pag129-8.png\" class=\"alignright size-full wp-image-13274\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8.png\" alt=\"\" width=\"235\" height=\"220\" \/><\/a>Na figura, est\u00e1 representada uma circunfer\u00eancia de centro O e nela quatro pontos A, B, C e D, tais que \\(\\overline {AB} = \\overline {CD} \\).<\/p>\n<ol>\n<li>Numa circunfer\u00eancia, a cordas iguais correspondem arcos iguais e vice-versa. Logo, como as cordas [AB] e [CD] s\u00e3o iguais, ent\u00e3o tamb\u00e9m s\u00e3o iguais os arcos AB e CD. Consequentemente, tamb\u00e9m ser\u00e3o iguais os arcos BD e AC. Logo, as cordas correspondentes a estes arcos tamb\u00e9m ser\u00e3o iguais, pelo que ser\u00e1 \\(\\overline {BD} = \\overline {AC} \\).<br \/>\n\u00ad<\/li>\n<li>Como a amplitude do arco maior BC \u00e9 185\u00ba, ent\u00e3o a amplitude do arco menor BC \u00e9 175\u00ba, isto \u00e9,\u00a0\\(\\overparen{BA} + \\overparen{AD} + \\overparen{DC} = 175^\\circ \\).<br \/>\nComo os arcos BA e DC s\u00e3o iguais e a amplitude do arco AD \u00e9 80\u00ba, resulta\u00a0\\(\\overparen{BA} = \\overparen{DC} = \\frac{{95^\\circ }}{2} = 47,5^\\circ \\).<br \/>\nLogo,\u00a0\\(C\\widehat AD = \\frac{{\\overparen{DC}}}{2} = \\frac{{47,5^\\circ }}{2} = 23,75^\\circ \\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13272' onClick='GTTabs_show(0,13272)'>&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 O e nela quatro pontos A, B, C e D, tais que \\(\\overline {AB} = \\overline {CD} \\). Justifica que \\(\\overline {BD} =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20455,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[213,97,278],"tags":[426,280,188],"series":[],"class_list":["post-13272","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-inscrito","tag-circunferencia"],"views":2688,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag129-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13272","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=13272"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13272\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20455"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13272"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}