{"id":14354,"date":"2018-04-10T21:36:24","date_gmt":"2018-04-10T20:36:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14354"},"modified":"2022-01-11T14:42:55","modified_gmt":"2022-01-11T14:42:55","slug":"duas-retas-e-uma-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14354","title":{"rendered":"Duas retas e uma circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_14354' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14354' class='GTTabs_curr'><a  id=\"14354_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14354' ><a  id=\"14354_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_14354'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14357\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14357\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12.png\" data-orig-size=\"415,384\" 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\/9V2Pag71-12.png\" class=\"alignright size-medium wp-image-14357\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12-300x278.png\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12-300x278.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12.png 415w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Na figura, est\u00e3o representadas as retas <em>AD<\/em> e <em>CD<\/em> e a circunfer\u00eancia de di\u00e2metro [<em>AC<\/em>].<br \/>\nO ponto <em>B<\/em> pertence \u00e0 circunfer\u00eancia e \u00e0 reta <em>AD<\/em>.<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>a reta <em>CD<\/em> \u00e9 tangente \u00e0 circunfer\u00eancia no ponto <em>C<\/em>;<\/li>\n<li>\\(C\\widehat DA = 50^\\circ \\);<\/li>\n<li>\\(\\overline {CD} = 8\\) cm.<\/li>\n<\/ul>\n<p>A figura n\u00e3o est\u00e1 desenhada \u00e0 escala.<\/p>\n<ol>\n<li>Qual \u00e9 a amplitude, em graus, do arco <em>CB<\/em>?<br \/>\n[A]\u00a0\\(60^\\circ \\)<br \/>\n[B]\u00a0\\(70^\\circ \\)<br \/>\n[C]\u00a0\\(80^\\circ \\)<br \/>\n[D]\u00a0\\(90^\\circ \\)<\/li>\n<li>Determina\u00a0\\(\\overline {CA} \\).<br \/>\nApresenta o resultado em cent\u00edmetros, arredondado \u00e0s d\u00e9cimas.<br \/>\nApresenta todos os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14354' onClick='GTTabs_show(1,14354)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14354'>\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\/9V2Pag71-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14357\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14357\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12.png\" data-orig-size=\"415,384\" 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\/9V2Pag71-12.png\" class=\"alignright size-medium wp-image-14357\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12-300x278.png\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12-300x278.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12.png 415w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Sabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote><p>a reta <em>CD<\/em> \u00e9 tangente \u00e0 circunfer\u00eancia no ponto <em>C<\/em>;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(C\\widehat DA = 50^\\circ \\);<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(\\overline {CD} = 8\\) cm.<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<ol>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [<em>ACD<\/em>], os \u00e2ngulos <em>CAD<\/em> e <em>ADC<\/em> s\u00e3o complementares. Logo, \\(C\\widehat AD = 90^\\circ &#8211; A\\widehat DC = 90^\\circ &#8211; 50^\\circ = 40^\\circ \\).<br \/>\nAssim, tendo em considera\u00e7\u00e3o que <em>CAD<\/em> \u00e9 um \u00e2ngulo inscrito, temos: \\(BC = 2 \\times C\\widehat AD = 2 \\times 40^\\circ = 80^\\circ \\).<br \/>\nPortanto, a alternativa correta \u00e9 a [C].<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [<em>ACD<\/em>], temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} A\\widehat DC = \\frac{{\\overline {CA} }}{{\\overline {CD} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 50^\\circ = \\frac{{\\overline {CA} }}{8}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {CA} = 8 \\times {\\mathop{\\rm tg}\\nolimits} 50^\\circ }\\\\{}&amp;{}&amp;{\\overline {CA} \\approx 9,5}\\end{array}\\]<br \/>\nPortanto,\u00a0\\(\\overline {CA} \\approx 9,5\\) cm.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14354' onClick='GTTabs_show(0,14354)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representadas as retas AD e CD e a circunfer\u00eancia de di\u00e2metro [AC]. O ponto B pertence \u00e0 circunfer\u00eancia e \u00e0 reta AD. Sabe-se que: a reta CD \u00e9&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14358,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[280,491,493,490,492],"series":[],"class_list":["post-14354","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-angulo-inscrito","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":1944,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag71-12a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14354","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=14354"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14354\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14358"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14354"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}