{"id":13212,"date":"2018-01-10T17:42:33","date_gmt":"2018-01-10T17:42:33","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13212"},"modified":"2022-01-16T22:37:51","modified_gmt":"2022-01-16T22:37:51","slug":"observa-a-figura-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13212","title":{"rendered":"Observa a figura"},"content":{"rendered":"<p><ul id='GTTabs_ul_13212' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13212' class='GTTabs_curr'><a  id=\"13212_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13212' ><a  id=\"13212_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_13212'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13213\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13213\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1.png\" data-orig-size=\"245,285\" 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\/9V1Pag123-1.png\" class=\"alignright wp-image-13213\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1.png\" alt=\"\" width=\"200\" height=\"233\" \/><\/a>Observa a figura.<\/p>\n<p>Sabendo que o raio da circunfer\u00eancia \u00e9 5 cm e que\u00a0\\(\\overline {AB} = 8\\) cm, calcula\u00a0\\(\\overline {OM} \\).<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13212' onClick='GTTabs_show(1,13212)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13212'>\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\/9V1Pag123-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13213\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13213\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1.png\" data-orig-size=\"245,285\" 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\/9V1Pag123-1.png\" class=\"alignright wp-image-13213\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1.png\" alt=\"\" width=\"200\" height=\"233\" \/><\/a>Consideremos tri\u00e2ngulos ret\u00e2ngulos [AMO] e [BMO], que possuem um cateto comum, o cateto [OM], e iguais hipotenusas, pois\u00a0\\(\\overline {AO} = \\overline {BO} \\).<\/p>\n<p>Assim sendo, os dois tri\u00e2ngulos ter\u00e3o tamb\u00e9m iguais os segundos catetos, sendo \\(\\overline {AM} = \\overline {BM} = \\frac{{\\overline {AB} }}{2}\\).<\/p>\n<p>Desta forma, resulta que M \u00e9 o ponto m\u00e9dio do segmento de reta [AB] e, consequentemente, a reta r \u00e9 a mediatriz da corda [AB].<\/p>\n<p>Assim, aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [AMO], temos \\(\\overline {OM} = \\sqrt {{{\\overline {AO} }^2} &#8211; {{\\overline {AM} }^2}} = \\sqrt {{5^2} &#8211; {4^2}} = \\sqrt 9 = 3\\) cm.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13212' onClick='GTTabs_show(0,13212)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura. Sabendo que o raio da circunfer\u00eancia \u00e9 5 cm e que\u00a0\\(\\overline {AB} = 8\\) cm, calcula\u00a0\\(\\overline {OM} \\). Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20436,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,188],"series":[],"class_list":["post-13212","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-circunferencia"],"views":2716,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13212","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=13212"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13212\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20436"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13212"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}