{"id":13301,"date":"2018-01-18T00:25:34","date_gmt":"2018-01-18T00:25:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13301"},"modified":"2022-01-17T00:27:24","modified_gmt":"2022-01-17T00:27:24","slug":"determina-o-valor-de-x-em-cada-caso","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13301","title":{"rendered":"Determina o valor de x em cada caso"},"content":{"rendered":"<p><ul id='GTTabs_ul_13301' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13301' class='GTTabs_curr'><a  id=\"13301_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13301' ><a  id=\"13301_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_13301'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13302\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13302\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png\" data-orig-size=\"370,885\" 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\/9V1Pag132-5.png\" class=\"alignright wp-image-13302\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5-125x300.png\" alt=\"\" width=\"300\" height=\"718\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5-125x300.png 125w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png 370w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Determina o valor de x em cada caso<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13301' onClick='GTTabs_show(1,13301)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13301'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13302\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13302\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png\" data-orig-size=\"370,885\" 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\/9V1Pag132-5.png\" class=\"alignright wp-image-13302\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5-125x300.png\" alt=\"\" width=\"300\" height=\"718\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5-125x300.png 125w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5.png 370w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Tendo em considera\u00e7\u00e3o que o \u00e2ngulo CBD \u00e9 um \u00e2ngulo ex-inscrito, vem:\u00a0\\[x = C\\widehat BD = \\frac{{\\overparen{BD} + \\overparen{BE}}}{2} = \\frac{{100^\\circ + 140^\\circ }}{2} = 120^\\circ \\]<br \/>\nEm alternativa, temos: \\[\\begin{array}{l}x = C\\widehat BD = 180^\\circ &#8211; D\\widehat BE = 180^\\circ &#8211; \\frac{{\\overparen{DE}}}{2} = \\\\ = 180^\\circ &#8211; \\frac{{360^\\circ &#8211; \\left( {100^\\circ + 140^\\circ } \\right)}}{2} = 120^\\circ \\end{array}\\]<\/li>\n<li>\\[x = C\\widehat BD = 180^\\circ &#8211; D\\widehat BE = 180^\\circ &#8211; \\frac{{\\overparen{DE}}}{2} = 180^\\circ &#8211; \\frac{{40^\\circ }}{2} = 160^\\circ \\]<br \/>\n\u00ad<br \/>\n\u00ad<br \/>\n\u00ad<\/li>\n<li>Como o \u00e2ngulo CBD \u00e9 um \u00e2ngulo ex-inscrito, ent\u00e3o\u00a0\\(C\\widehat BD = \\frac{{\\overparen{BD} + \\overparen{BE}}}{2}\\).<br \/>\nLogo, substituindo pelos valores conhecidos, vem:<br \/>\n\\[\\begin{array}{*{20}{c}}{95^\\circ = \\frac{{x + 80^\\circ }}{2}}&amp; \\Leftrightarrow &amp;{x = 110^\\circ }\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13301' onClick='GTTabs_show(0,13301)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina o valor de x em cada caso Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20462,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,461,188],"series":[],"class_list":["post-13301","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-angulo-ex-inscrito","tag-circunferencia"],"views":3356,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag132-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13301","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=13301"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13301\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20462"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13301"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}