{"id":122129,"date":"2019-02-14T10:53:53","date_gmt":"2019-02-14T12:53:53","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=122129"},"modified":"2020-10-31T15:02:48","modified_gmt":"2020-10-31T18:02:48","slug":"applet-duas-lunulas-coloridas","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/applet-duas-lunulas-coloridas\/","title":{"rendered":". Applet: Duas l\u00fanulas coloridas"},"content":{"rendered":"<div style=\"border: 8px double #800000; padding: 5px;padding-left: 8px; padding-right: 8px;\">\n<p style=\"margin:20px\">\n<p class=\"tis c3\">Problema- Duas l\u00fanulas coloridas<\/p>\n<p style=\"margin:30px\">\n<div class=\"g1\" style=\"line-height:25px; width:77%; margin-left:auto; margin-right:auto\">\n<p class=\"tit\">Problema<\/p>\n<hr\/>\n<p style=\"margin:20px\">\n<p><strong>(a)<\/strong> A figura abaixo mostra um tri\u00e2ngulo ret\u00e2ngulo de catetos [tex]6 \\,  [\/tex]cm e [tex] \\, 8 \\, [\/tex]cm  e tr\u00eas semicircunfer\u00eancias tendo os lados desse tri\u00e2ngulo como di\u00e2metros. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_02.png\" style=\"border: none;\"alt=\"\" width=\"372\" height=\"208\" style=\"border: none;\" class=\"aligncenter size-full wp-image-112461\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_02.png 372w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_02-300x168.png 300w\" sizes=\"auto, (max-width: 372px) 100vw, 372px\" \/><br \/>\nDetermine a soma das \u00e1reas das duas l\u00fanulas coloridas.<\/p>\n<p style=\"margin:10px;\">\n<p><strong>(b)<\/strong> Tente estabelecer o caso geral da soma das \u00e1reas de  duas l\u00fanulas definidas por arcos cujos di\u00e2metros s\u00e3o os lados de um tri\u00e2ngulo ret\u00e2ngulo de catetos com comprimentos [tex]b \\,  [\/tex] e [tex] \\, c[\/tex] e hipotenusa medindo [tex] \\, a.[\/tex]<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_04.png\" style=\"border: none;\" alt=\"\" width=\"465\" height=\"300\" style=\"border: none;\" class=\"aligncenter size-full wp-image-112759\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_04.png 465w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2018\/09\/prob252_04-300x194.png 300w\" sizes=\"auto, (max-width: 465px) 100vw, 465px\" \/><\/p>\n<p style=\"margin:20px\">\n<\/div>\n<p style=\"margin:50px\">\n<hr style=\"height:4px;background-color:#800000; border: 0 none\"\/>\n<p style=\"margin:50px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:70%x;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:70%px;background-color: #FFF5EE; padding:15px; font-family: Garamond;font-size: 16px;color: #616161;\">Observar a constru\u00e7\u00e3o das l\u00fanulas pode lhe ajudar a estabelecer uma estrat\u00e9gia para resolver o problema!<\/p>\n<p style=\"margin:10px\">\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:30px\">\n<div style=\"border: 3px solid #800000; text-align:justify; padding: 20px;width:87%; margin-left: auto; margin-right: auto;\" >\nVoc\u00ea pode visualizar a constru\u00e7\u00e3o das duas l\u00fanulas do problema utilizando o <em>applet <\/em> abaixo. Para isso \u00e9 s\u00f3 esperar o aplicativo carregar completamente e clicar sucessivamente nos quadradinhos que ir\u00e3o aparecer.<br \/>\nPara retornar \u00e0 configura\u00e7\u00e3o inicial, clique nas setinhas que aparecem no canto superior direito do aplicativo. <\/p>\n<p style=\"text-align:center; line-height:20px;\">\n<iframe loading=\"lazy\" title=\"L\u00fanulas coloridas\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ndga2jem\/width\/649\/height\/696\/border\/ffffff\/sfsb\/false\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"650px\" height=\"696px\" style=\"border: 1px solid #800000;\"> <\/iframe><br \/>\n<span style=\"font-size:14px\">OBMEP_srg, criado com o <a href=\"http:\/\/www.geogebra.org\/\" target=\"_blank\" >GeoGebra<\/a><\/span><\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:30px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:370px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:250px;background-color: #FFF5EE; padding:15px; font-family: Georgia; font-size: 16px;color: #616161;\"> Para ver uma solu\u00e7\u00e3o do problema, clique <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=118405\" title=\"Ver a solu\u00e7\u00e3o.\" target=\"_blank\"><strong> AQUI<\/strong><\/a>. <\/span>\n<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<hr style=\"height:1px;background-color:#800000;margin-top: 6px; margin-bottom: 6px;  border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#800000; margin-top: 6px; margin-bottom: 6px; border: 0 none\"\/>\n<p style=\"text-align: right;\"><span style=\"color: #800000; font-size: 20px;\"><strong>Equipe COM &#8211; OBMEP<\/strong><\/span><\/p>\n<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema- Duas l\u00fanulas coloridas Problema (a) A figura abaixo mostra um tri\u00e2ngulo ret\u00e2ngulo de catetos [tex]6 \\, [\/tex]cm e [tex] \\, 8 \\, [\/tex]cm e tr\u00eas semicircunfer\u00eancias tendo os lados desse tri\u00e2ngulo como di\u00e2metros. Determine a soma das \u00e1reas das duas l\u00fanulas coloridas. (b) Tente estabelecer o caso geral da soma das \u00e1reas de duas &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/applet-duas-lunulas-coloridas\/\">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-122129","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/122129","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=122129"}],"version-history":[{"count":12,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/122129\/revisions"}],"predecessor-version":[{"id":122137,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/122129\/revisions\/122137"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=122129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}