{"id":13224,"date":"2018-01-10T22:03:03","date_gmt":"2018-01-10T22:03:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13224"},"modified":"2022-01-16T23:04:27","modified_gmt":"2022-01-16T23:04:27","slug":"duas-retas-tangentes-a-uma-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13224","title":{"rendered":"Duas retas tangentes a uma circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13224' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13224' class='GTTabs_curr'><a  id=\"13224_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13224' ><a  id=\"13224_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_13224'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13225\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13225\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4.png\" data-orig-size=\"450,250\" 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\/9V1Pag123-4.png\" class=\"alignright size-medium wp-image-13225\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4-300x167.png\" alt=\"\" width=\"300\" height=\"167\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4-300x167.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4.png 450w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Sabendo que as retas PA e PB s\u00e3o tangentes \u00e0 circunfer\u00eancia e que \\(\\overparen{AB} = 140^\\circ \\), determina as amplitudes dos quatro \u00e2ngulos internos do quadril\u00e1tero [OAPB].<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13224' onClick='GTTabs_show(1,13224)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13224'>\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\/9V1Pag123-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13225\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13225\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4.png\" data-orig-size=\"450,250\" 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\/9V1Pag123-4.png\" class=\"alignright size-medium wp-image-13225\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4-300x167.png\" alt=\"\" width=\"300\" height=\"167\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4-300x167.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4.png 450w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Como a reta tangente a uma circunfer\u00eancia \u00e9 perpendicular ao raio no ponto de tang\u00eancia, ent\u00e3o\u00a0\\(O\\widehat AP = O\\widehat BP = 90^\\circ \\).<\/p>\n<p>Por outro lado,\u00a0\\(A\\widehat OB = \\overparen{AB} = 140^\\circ \\).<\/p>\n<p>Finalmente, como a soma das amplitudes dos \u00e2ngulos internos de um quadril\u00e1tero \u00e9 igual a \\(180^\\circ \\), vem\u00a0\\(A\\widehat PB = 360^\\circ &#8211; \\left( {90^\\circ + 90^\\circ + 140^\\circ } \\right) = 40^\\circ \\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13224' onClick='GTTabs_show(0,13224)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabendo que as retas PA e PB s\u00e3o tangentes \u00e0 circunfer\u00eancia e que \\(\\overparen{AB} = 140^\\circ \\), determina as amplitudes dos quatro \u00e2ngulos internos do quadril\u00e1tero [OAPB]. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20441,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,188,282],"series":[],"class_list":["post-13224","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-circunferencia","tag-tangente-a-uma-circunferencia"],"views":2514,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13224","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=13224"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13224\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20441"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13224"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}