{"id":10153,"date":"2012-10-06T01:07:41","date_gmt":"2012-10-06T00:07:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10153"},"modified":"2022-01-20T22:37:39","modified_gmt":"2022-01-20T22:37:39","slug":"duas-circunferencias-concentricas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10153","title":{"rendered":"Duas circunfer\u00eancias conc\u00eantricas"},"content":{"rendered":"<p><ul id='GTTabs_ul_10153' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10153' class='GTTabs_curr'><a  id=\"10153_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10153' ><a  id=\"10153_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_10153'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Os raios de duas circunfer\u00eancias conc\u00eantricas medem $4$ cm e $5$ cm.<\/p>\n<p>Determine o comprimento da corda da circunfer\u00eancia maior que \u00e9 tangente \u00e0 circunfer\u00eancia menor.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10153' onClick='GTTabs_show(1,10153)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10153'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":253,\r\n\"height\":305,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<p>Consideremos a\u00a0constru\u00e7\u00e3o acima, que ilustra a situa\u00e7\u00e3o descrita.<\/p>\n<p>O tri\u00e2ngulo [OAT] \u00e9 ret\u00e2ngulo em T, pois uma reta tangente a uma circunfer\u00eancia \u00e9 perpendicular ao raio dirigido ao ponto de tang\u00eancia.<\/p>\n<p>Logo, de acordo com o Teorema de Pit\u00e1goras, resulta $\\overline {AT}\u00a0 = 3$ cm.<\/p>\n<p>Sabe-se ainda que toda a reta que \u00e9 perpendicular a uma corda e cont\u00e9m o centro de uma circunfer\u00eancia bisseta essa corda.<\/p>\n<p>Logo, $\\overline {AB}\u00a0 = 2 \\times \\overline {AT}\u00a0 = 2 \\times 3 = 6$ cm.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10153' onClick='GTTabs_show(0,10153)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Os raios de duas circunfer\u00eancias conc\u00eantricas medem $4$ cm e $5$ cm. Determine o comprimento da corda da circunfer\u00eancia maior que \u00e9 tangente \u00e0 circunfer\u00eancia menor. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20786,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,67,430],"series":[],"class_list":["post-10153","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-geometria","tag-modulo-inicial"],"views":2637,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag038-27_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10153","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=10153"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10153\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20786"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10153"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}