{"id":13310,"date":"2018-01-24T23:34:49","date_gmt":"2018-01-24T23:34:49","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13310"},"modified":"2022-01-17T00:31:29","modified_gmt":"2022-01-17T00:31:29","slug":"um-angulo-de-vertice-exterior-a-um-circulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13310","title":{"rendered":"Um \u00e2ngulo de v\u00e9rtice exterior a um c\u00edrculo"},"content":{"rendered":"<p><ul id='GTTabs_ul_13310' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13310' class='GTTabs_curr'><a  id=\"13310_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13310' ><a  id=\"13310_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_13310'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13311\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13311\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1.png\" data-orig-size=\"340,310\" 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\/9V1Pag135-1.png\" class=\"alignright size-medium wp-image-13311\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1-300x274.png\" alt=\"\" width=\"300\" height=\"274\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1-300x274.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1.png 340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Determina \\(A\\widehat VD\\), sabendo que \\(\\overparen{AD} = 100^\\circ \\) e \\(\\overparen{BC} = 40^\\circ \\).<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13310' onClick='GTTabs_show(1,13310)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13310'>\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\/9V1Pag135-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13311\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13311\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1.png\" data-orig-size=\"340,310\" 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\/9V1Pag135-1.png\" class=\"alignright size-medium wp-image-13311\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1-300x274.png\" alt=\"\" width=\"300\" height=\"274\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1-300x274.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1.png 340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Tendo em considera\u00e7\u00e3o que o \u00e2ngulo AVD \u00e9 um \u00e2ngulo com v\u00e9rtice exterior a um c\u00edrculo, vem:<\/p>\n<p>\\[A\\widehat VD = \\frac{{\\overparen{AD} &#8211; \\overparen{BC}}}{2} = \\frac{{100^\\circ &#8211; 40^\\circ }}{2} = 30^\\circ \\]<\/p>\n<\/p>\n<p><span style=\"text-decoration: underline;\">ALTERNATIVA<\/span>:<\/p>\n<p>Tracemos a corda [AC] e reparemos que o \u00e2ngulo ACD \u00e9 um \u00e2ngulo externo do tri\u00e2ngulo [ACV].<\/p>\n<p>Assim, temos:<\/p>\n<p>\\[A\\widehat VD = A\\widehat CD &#8211; C\\widehat AV = \\frac{{\\overparen{AD}}}{2} &#8211; \\frac{{\\overparen{BC}}}{2} = \\frac{{\\overparen{AD} &#8211; \\overparen{BC}}}{2} = \\frac{{100^\\circ &#8211; 40^\\circ }}{2} = 30^\\circ \\]<\/p>\n<p><strong>Nota<\/strong>: A amplitude de um \u00e2ngulo externo de um tri\u00e2ngulo \u00e9 igual \u00e0 soma das amplitudes dos \u00e2ngulos internos n\u00e3o adjacentes.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13310' onClick='GTTabs_show(0,13310)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina \\(A\\widehat VD\\), sabendo que \\(\\overparen{AD} = 100^\\circ \\) e \\(\\overparen{BC} = 40^\\circ \\). Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20463,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,462,280,188],"series":[],"class_list":["post-13310","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-de-vertice-exterior-a-um-circulo","tag-angulo-inscrito","tag-circunferencia"],"views":1949,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag135-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13310","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=13310"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13310\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20463"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13310"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}