{"id":13533,"date":"2014-02-02T01:45:51","date_gmt":"2014-02-02T03:45:51","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=13533"},"modified":"2023-01-18T23:36:07","modified_gmt":"2023-01-19T02:36:07","slug":"problema-olimpico-nivel-c-circunferencias-e-areas","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-olimpico-nivel-c-circunferencias-e-areas\/","title":{"rendered":".Problema Ol\u00edmpico &#8211; N\u00edvel C: Circunfer\u00eancias e \u00e1reas"},"content":{"rendered":"<div style=\"border: 3px solid #800000; padding: 8px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\"><span style=\"font-family: 'Georgia'; font-size: 20px; color: #616161;\"><strong>Problema<\/strong><\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"text-align: justify; padding-left: 12px; font-family: verdana; color: #616161; font-size: 15px; line-height: 25px;\">Na figura, as tr\u00eas circunfer\u00eancias t\u00eam o mesmo centro e seus raios s\u00e3o [tex]8 \\, \\text{cm},\\, a\\,\\text{cm},\\, 17 \\,\\text{cm}[\/tex], com [tex]8\\lt\\,a\\,\\lt17[\/tex].<br \/>\nDetermine [tex]a[\/tex], sabendo as \u00e1reas das regi\u00f5es sombreadas <strong>R<\/strong> e <strong>S<\/strong> s\u00e3o iguais.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/02\/fig6.png\" style=\"border: 0px;\" alt=\"fig6\" width=\"284\" height=\"267\" class=\"aligncenter size-full wp-image-13534\" \/>\n<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div style=\"border: 3px  solid  #800000; padding: 8px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\"><span style=\"font-family: 'Georgia'; font-size: 20px; color: #616161;\"><strong>Solu\u00e7\u00e3o <\/strong><\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"text-align: justify; padding-left: 12px; font-family: verdana; color: #616161; font-size: 15px; line-height: 30px;\">Veja que a \u00e1rea da regi\u00e3o [tex]R[\/tex] \u00e9<br \/>\n [tex]\\qquad A_{R}=64\\pi[\/tex].<br \/>\nJ\u00e1 a \u00e1rea da regi\u00e3o [tex]S[\/tex] \u00e9<br \/>\n [tex]\\qquad A_{S}=289\\pi-a^2\\pi=(289-a^2)\\pi[\/tex].<br \/>\nComo [tex]A_{R}=A_{S}[\/tex], ent\u00e3o [tex](289-a^2)\\pi=64\\pi[\/tex].<br \/>\nAssim, [tex]289-64=a^2[\/tex], donde [tex] 225=a^2[\/tex] e, portanto,  [tex] \\fbox{$a=15\\text{ cm}$}[\/tex].<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pela aluna do PIC-OBMEP <strong>Noemi Zeraick Monteiro<\/strong>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema Na figura, as tr\u00eas circunfer\u00eancias t\u00eam o mesmo centro e seus raios s\u00e3o [tex]8 \\, \\text{cm},\\, a\\,\\text{cm},\\, 17 \\,\\text{cm}[\/tex], com [tex]8\\lt\\,a\\,\\lt17[\/tex]. Determine [tex]a[\/tex], sabendo as \u00e1reas das regi\u00f5es sombreadas R e S s\u00e3o iguais. &nbsp; Solu\u00e7\u00e3o Veja que a \u00e1rea da regi\u00e3o [tex]R[\/tex] \u00e9 [tex]\\qquad A_{R}=64\\pi[\/tex]. J\u00e1 a \u00e1rea da regi\u00e3o [tex]S[\/tex] \u00e9 [tex]\\qquad &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-olimpico-nivel-c-circunferencias-e-areas\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-13533","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/13533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=13533"}],"version-history":[{"count":30,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/13533\/revisions"}],"predecessor-version":[{"id":182982,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/13533\/revisions\/182982"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=13533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}