{"id":13427,"date":"2018-02-02T20:58:14","date_gmt":"2018-02-02T20:58:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13427"},"modified":"2022-01-17T15:15:50","modified_gmt":"2022-01-17T15:15:50","slug":"a-reta-bc-e-tangente-a-circunferencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13427","title":{"rendered":"A reta BC \u00e9 tangente \u00e0 circunfer\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13427' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13427' class='GTTabs_curr'><a  id=\"13427_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13427' ><a  id=\"13427_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_13427'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13429\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13429\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8.png\" data-orig-size=\"275,215\" 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\/02\/9V1Pag144-8.png\" class=\"alignright size-full wp-image-13429\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8.png\" alt=\"\" width=\"275\" height=\"215\" \/><\/a>A reta BC \u00e9 tangente \u00e0 circunfer\u00eancia de centro O.<\/p>\n<p>Quais s\u00e3o os valores das medidas de amplitude x, y e z, dos \u00e2ngulos assinalados?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13427' onClick='GTTabs_show(1,13427)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13427'>\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\/02\/9V1Pag144-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13429\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13429\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8.png\" data-orig-size=\"275,215\" 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\/02\/9V1Pag144-8.png\" class=\"alignright size-full wp-image-13429\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8.png\" alt=\"\" width=\"275\" height=\"215\" \/><\/a>Tendo em considera\u00e7\u00e3o que a amplitude de um \u00e2ngulo inscrito \u00e9 igual a metade da amplitude do arco compreendido entre os seus lados, vem:<\/p>\n<p>\\[x = S\\widehat OR = \\overparen{SR} = 2 \\times S\\widehat PR = 2 \\times 46^\\circ = 92^\\circ \\]<\/p>\n<p>\\[y = S\\widehat QR = \\frac{{\\overparen{SR}}}{2} = \\frac{{92^\\circ }}{2} = 46^\\circ \\]<\/p>\n<p>\\[S\\widehat BR = \\frac{{\\overparen{SPR}}}{2} = \\frac{{360^\\circ &#8211; \\overparen{SR}}}{2} = \\frac{{360^\\circ &#8211; 92^\\circ }}{2} = 134^\\circ \\]<\/p>\n<p>Finalmente, temos:<\/p>\n<p>\\[z = R\\widehat BC = 180^\\circ &#8211; S\\widehat BD &#8211; S\\widehat BR = 180^\\circ &#8211; 29^\\circ &#8211; 134^\\circ = 17^\\circ \\]<\/p>\n<\/p>\n<p>ALTERNATIVA:<br \/>\nTendo em considera\u00e7\u00e3o que os \u00e2ngulos SBD e RBC s\u00e3o \u00e2ngulos de segmento, vem:<\/p>\n<p>\\[z = R\\widehat BC = \\frac{{\\overparen{BR}}}{2} = \\frac{{\\overparen{SR} &#8211; \\overparen{SB}}}{2} = \\frac{{92^\\circ &#8211; 2 \\times S\\widehat BD}}{2} = \\frac{{92^\\circ &#8211; 2 \\times 29^\\circ }}{2} = 17^\\circ \\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13427' onClick='GTTabs_show(0,13427)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A reta BC \u00e9 tangente \u00e0 circunfer\u00eancia de centro O. Quais s\u00e3o os valores das medidas de amplitude x, y e z, dos \u00e2ngulos assinalados? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20496,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[279,459,280,188],"series":[],"class_list":["post-13427","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-angulo-ao-centro","tag-angulo-de-segmento","tag-angulo-inscrito","tag-circunferencia"],"views":2721,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13427","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=13427"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13427\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20496"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13427"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13427"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13427"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}