{"id":13435,"date":"2018-02-02T22:05:37","date_gmt":"2018-02-02T22:05:37","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13435"},"modified":"2022-01-17T15:29:19","modified_gmt":"2022-01-17T15:29:19","slug":"um-angulo-de-vertice-exterior-a-um-circulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13435","title":{"rendered":"Um \u00e2ngulo de v\u00e9rtice exterior a um c\u00edrculo"},"content":{"rendered":"<p><ul id='GTTabs_ul_13435' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13435' class='GTTabs_curr'><a  id=\"13435_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13435' ><a  id=\"13435_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_13435'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13436\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13436\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" data-orig-size=\"275,295\" 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-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" class=\"alignright size-full wp-image-13436\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" alt=\"\" width=\"275\" height=\"295\" \/><\/a>Sabendo que \\(\\overparen{AB} = 30^\\circ \\) e \\(\\overparen{CD} = 90^\\circ \\), determina a amplitude do \u00e2ngulo CPD.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13435' onClick='GTTabs_show(1,13435)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13435'>\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\/02\/9V1Pag144-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13436\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13436\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" data-orig-size=\"275,295\" 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-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" class=\"alignright size-full wp-image-13436\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9.png\" alt=\"\" width=\"275\" height=\"295\" \/><\/a>Tendo em considera\u00e7\u00e3o que o \u00e2ngulo CAD \u00e9 um \u00e2ngulo externo do tri\u00e2ngulo [ADP], temos:<\/p>\n<p>\\[C\\widehat PD = C\\widehat AD &#8211; A\\widehat DP = \\frac{{\\overparen{CD}}}{2} &#8211; \\frac{{\\overparen{AB}}}{2} = \\frac{{90^\\circ }}{2} &#8211; \\frac{{30^\\circ }}{2} = 30^\\circ \\]<\/p>\n<p>ALTERNATIVA:<br \/>\nTendo em considera\u00e7\u00e3o que o \u00e2ngulo CPD \u00e9 um\u00a0 \u00e2ngulo de v\u00e9rtice exterior a um c\u00edrculo, vem:<\/p>\n<p>\\[C\\widehat DP = \\frac{{\\overparen{CD} &#8211; \\overparen{AB}}}{2} = \\frac{{90^\\circ &#8211; 30^\\circ }}{2} = 30^\\circ \\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13435' onClick='GTTabs_show(0,13435)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que \\(\\overparen{AB} = 30^\\circ \\) e \\(\\overparen{CD} = 90^\\circ \\), determina a amplitude do \u00e2ngulo CPD. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20497,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[462,280,188],"series":[],"class_list":["post-13435","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-angulo-de-vertice-exterior-a-um-circulo","tag-angulo-inscrito","tag-circunferencia"],"views":2089,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13435","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=13435"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13435\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20497"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13435"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}