{"id":14319,"date":"2018-04-09T21:21:57","date_gmt":"2018-04-09T20:21:57","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14319"},"modified":"2022-01-11T14:29:58","modified_gmt":"2022-01-11T14:29:58","slug":"um-retangulo-inscrito-numa-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14319","title":{"rendered":"Um ret\u00e2ngulo inscrito numa circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_14319' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14319' class='GTTabs_curr'><a  id=\"14319_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14319' ><a  id=\"14319_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_14319'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14320\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14320\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png\" data-orig-size=\"358,330\" 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\/9V2Pag69-7.png\" class=\"alignright wp-image-14320\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7-300x277.png\" alt=\"\" width=\"240\" height=\"221\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7-300x277.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png 358w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Na figura, est\u00e1 representada uma circunfer\u00eancia de centro <em>O<\/em>, na qual est\u00e1 inscrito um ret\u00e2ngulo [<em>ABCD<\/em>].<br \/>\nA figura n\u00e3o est\u00e1 desenhada \u00e0 escala.<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>\\(B\\widehat DA = 70^\\circ \\);<\/li>\n<li>\\(\\overline {AB} = 4,35\\) cm.<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 a amplitude, em graus, do arco <em>AB<\/em>?<\/li>\n<li>Quantos eixos de simetria tem o ret\u00e2ngulo [<em>ABCD<\/em>]?<\/li>\n<li>Qual \u00e9 o comprimento, em cent\u00edmetros, do di\u00e2metro [<em>BD<\/em>] da circunfer\u00eancia?<br \/>\nApresenta os c\u00e1lculos que efetuaste.<br \/>\nEscreve o resultado aproximado \u00e0s cent\u00e9simas.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14319' onClick='GTTabs_show(1,14319)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14319'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14320\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14320\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png\" data-orig-size=\"358,330\" 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\/9V2Pag69-7.png\" class=\"alignright wp-image-14320\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7-300x277.png\" alt=\"\" width=\"240\" height=\"221\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7-300x277.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7.png 358w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Tendo em considera\u00e7\u00e3o que <em>BDA<\/em> \u00e9 um \u00e2ngulo inscrito, vem:<br \/>\n\\(\\overparen{AB} = 2 \\times B\\widehat DA = 2 \\times 70^\\circ = 140^\\circ \\).<br \/>\n\u00ad<\/li>\n<li>O ret\u00e2ngulo [<em>ABCD<\/em>] tem dois eixos de simetria.<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABD<\/em>], temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} B\\widehat DA = \\frac{{\\overline {AB} }}{{\\overline {BD} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm sen}\\nolimits} 70^\\circ = \\frac{{4,35}}{{\\overline {BD} }}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BD} = \\frac{{4,35}}{{{\\mathop{\\rm sen}\\nolimits} 70^\\circ }}}\\\\{}&amp;{}&amp;{\\overline {BD} \\approx 4,63}\\end{array}\\]<br \/>\nPortanto, o di\u00e2metro [<em>BD<\/em>] da circunfer\u00eancia tem, aproximadamente, 4,63 cm de comprimento.<\/li>\n<\/ol><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14319' onClick='GTTabs_show(0,14319)'>&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 de centro O, na qual est\u00e1 inscrito um ret\u00e2ngulo [ABCD]. A figura n\u00e3o est\u00e1 desenhada \u00e0 escala. Sabe-se que: \\(B\\widehat DA = 70^\\circ \\); \\(\\overline&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14322,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,280,491,493,490,492],"series":[],"class_list":["post-14319","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-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":2060,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag69-7a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14319","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=14319"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14319\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14322"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14319"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14319"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14319"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}