{"id":14345,"date":"2018-04-10T20:26:20","date_gmt":"2018-04-10T19:26:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14345"},"modified":"2022-01-11T14:41:00","modified_gmt":"2022-01-11T14:41:00","slug":"uma-circunferencia-com-centro-no-ponto-o","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14345","title":{"rendered":"Uma circunfer\u00eancia com centro no ponto <em>O<\/em>"},"content":{"rendered":"<p><ul id='GTTabs_ul_14345' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14345' class='GTTabs_curr'><a  id=\"14345_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14345' ><a  id=\"14345_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_14345'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14347\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14347\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\" data-orig-size=\"282,289\" 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\/04\/9V2Pag71-11.png\" class=\"alignright wp-image-14347\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\" alt=\"\" width=\"240\" height=\"246\" \/><\/a>Na figura, est\u00e1 representada uma circunfer\u00eancia com centro no ponto <em>O<\/em>.<br \/>\nOs pontos <em>A<\/em>, <em>B<\/em> e <em>C<\/em> pertencem \u00e0 circunfer\u00eancia.<br \/>\nO ponto <em>P<\/em> pertence \u00e0 corda [<em>AC<\/em>].<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>os segmentos de reta [<em>AC<\/em>] e [<em>PB<\/em>] s\u00e3o perpendiculares;<\/li>\n<li>\\(B\\widehat AC = 65^\\circ \\);<\/li>\n<li>\\(\\overline {AP} = 1,6\\) cm.<\/li>\n<\/ul>\n<p>A figura n\u00e3o est\u00e1 desenhada \u00e0 escala.<\/p>\n<ol>\n<li>Qual \u00e9 o lugar geom\u00e9trico dos pontos do plano que distam 1,6 cm do ponto <em>A<\/em>?<\/li>\n<li>Determina\u00a0\\(\\overline {BP} \\).<br \/>\nApresenta o resultado em cent\u00edmetros, arredondado \u00e0s d\u00e9cimas.<br \/>\nApresenta todos os c\u00e1lculos que efetuares.<\/li>\n<li>Qual \u00e9 a amplitude, em graus, do \u00e2ngulo <em>BOC<\/em>?<br \/>\n[A]\u00a0\\(65^\\circ \\)<br \/>\n[B]\u00a0\\(100^\\circ \\)<br \/>\n[C]\u00a0\\(130^\\circ \\)<br \/>\n[D]\u00a0\\(195^\\circ \\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14345' onClick='GTTabs_show(1,14345)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14345'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14347\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14347\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\" data-orig-size=\"282,289\" 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\/04\/9V2Pag71-11.png\" class=\"alignright wp-image-14347\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11.png\" alt=\"\" width=\"240\" height=\"246\" \/><\/a>Sabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote><p>os segmentos de reta [<em>AC<\/em>] e [<em>PB<\/em>] s\u00e3o perpendiculares;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(B\\widehat AC = 65^\\circ \\);<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(\\overline {AP} = 1,6\\) cm.<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<ol>\n<li>O lugar geom\u00e9trico dos pontos do plano que distam 1,6 cm do ponto <em>A<\/em> \u00e9 a circunfer\u00eancia de centro <em>A<\/em> e raio \\(\\overline {AP} \\).<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABP<\/em>], vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} B\\widehat AC = \\frac{{\\overline {BP} }}{{\\overline {AP} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 65^\\circ = \\frac{{\\overline {BP} }}{{1,6}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BP} = 1,6 \\times {\\mathop{\\rm tg}\\nolimits} 65^\\circ }\\\\{}&amp;{}&amp;{\\overline {BP} \\approx 3,4}\\end{array}\\]<br \/>\nPortanto, \\(\\overline {BP} \\approx 3,4\\) cm.<br \/>\n\u00ad<\/li>\n<li>Como <em>BAC<\/em> \u00e9 um \u00e2ngulo inscrito, vem:\u00a0\\(B\\widehat OC = 2 \\times B\\widehat AC = 2 \\times 65^\\circ = 130^\\circ \\).<br \/>\nLogo, a alternativa correta \u00e9 a [C].<br \/>\n[C]\u00a0\\(130^\\circ \\)<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14345' onClick='GTTabs_show(0,14345)'>&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 com centro no ponto O. Os pontos A, B e C pertencem \u00e0 circunfer\u00eancia. O ponto P pertence \u00e0 corda [AC]. Sabe-se que: os segmentos&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14348,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,280,188,491,493,490,492],"series":[],"class_list":["post-14345","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-angulo-inscrito","tag-circunferencia","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":2110,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-11a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14345","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=14345"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14345\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14348"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14345"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14345"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14345"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}