{"id":13368,"date":"2018-01-29T14:45:47","date_gmt":"2018-01-29T14:45:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13368"},"modified":"2022-01-17T10:27:53","modified_gmt":"2022-01-17T10:27:53","slug":"determina-o-valor-de-x-e-de-y","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13368","title":{"rendered":"Determina o valor de $x$ e de $y$"},"content":{"rendered":"<p><ul id='GTTabs_ul_13368' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13368' class='GTTabs_curr'><a  id=\"13368_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13368' ><a  id=\"13368_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_13368'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13369\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13369\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6.png\" data-orig-size=\"365,825\" 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\/9V1Pag139-6.png\" class=\"alignright wp-image-13369\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6-133x300.png\" alt=\"\" width=\"240\" height=\"542\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6-133x300.png 133w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6.png 365w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Calcula, em cada caso, o valor de x e de y.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13368' onClick='GTTabs_show(1,13368)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13368'>\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\/9V1Pag139-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13369\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13369\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6.png\" data-orig-size=\"365,825\" 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\/9V1Pag139-6.png\" class=\"alignright wp-image-13369\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6-133x300.png\" alt=\"\" width=\"240\" height=\"542\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6-133x300.png 133w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6.png 365w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><strong>a)<\/strong><\/p>\n<p>Como os \u00e2ngulos s\u00e3o inscritos no mesmo arco capaz, ent\u00e3o s\u00e3o geometricamente iguais.<br \/>\nAssim,\u00a0\\(x = E\\widehat AD = y = E\\widehat CD = \\frac{{\\overparen{DE}}}{2} = E\\widehat BD = 35^\\circ \\).<\/p>\n<\/p>\n<p><strong>b)<\/strong><\/p>\n<p>Como o \u00e2ngulo BED \u00e9 um \u00e2ngulo externo do tri\u00e2ngulo [ADE], a sua amplitude \u00e9 igual \u00e0 soma das amplitudes dos \u00e2ngulos internos n\u00e3o adjacentes:\u00a0\\(x = B\\widehat ED = A\\widehat DE + D\\widehat AE = 24^\\circ + 48^\\circ = 72^\\circ \\).<\/p>\n<p>Como os \u00e2ngulos DEB e BEC s\u00e3o adjacentes suplementares, ent\u00e3o\u00a0\\(y = B\\widehat EC = 180^\\circ &#8211; B\\widehat ED = 180^\\circ &#8211; 72^\\circ = 108^\\circ \\).<\/p>\n<p><strong>c)<\/strong><\/p>\n<p>Como os \u00e2ngulos MON e MNO s\u00e3o \u00e2ngulos inscritos, ent\u00e3o as suas amplitudes s\u00e3o iguais \u00e0s amplitudes dos arcos compreendidos entre os seus lados.<\/p>\n<p>Assim,\u00a0\\(y = M\\widehat NO = \\frac{{\\overparen{PQO}}}{2} = \\frac{{50^\\circ + 80^\\circ }}{2} = 65^\\circ \\) e\u00a0\\(M\\widehat ON = \\frac{{\\overparen{NPQ}}}{2} = \\frac{{110^\\circ + 50^\\circ }}{2} = 80^\\circ \\).<\/p>\n<p>Finalmente, \\(M\\widehat NO = 180^\\circ &#8211; \\left( {M\\widehat NO + M\\widehat ON} \\right) = 180^\\circ &#8211; \\left( {65^\\circ + 80^\\circ } \\right) = 35^\\circ \\), pois a soma das amplitudes dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 igual a 180 graus.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13368' onClick='GTTabs_show(0,13368)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula, em cada caso, o valor de x e de y. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20476,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,280,188],"series":[],"class_list":["post-13368","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-inscrito","tag-circunferencia"],"views":2995,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag139-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13368","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=13368"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13368\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20476"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13368"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}