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<b>Notice</b>:  Function _load_textdomain_just_in_time was called <strong>incorrectly</strong>. Translation loading for the <code>health-check</code> domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the <code>init</code> action or later. Please see <a href="https://developer.wordpress.org/advanced-administration/debug/debug-wordpress/">Debugging in WordPress</a> for more information. (This message was added in version 6.7.0.) in <b>/home/acasinha/public_html/wp-includes/functions.php</b> on line <b>6131</b><br />
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<b>Notice</b>:  A função _load_textdomain_just_in_time foi chamada <strong>incorrectamente</strong>. O carregamento da tradução para o domínio <code>hueman</code> foi accionado demasiado cedo. Isto é normalmente um indicador de que algum código no plugin ou tema está a ser executado demasiado cedo. As traduções devem ser carregadas na acção <code>init</code> ou mais tarde. Por favor veja <a href="https://developer.wordpress.org/advanced-administration/debug/debug-wordpress/">Depuração no WordPress</a> para mais informações. (Esta mensagem foi adicionada na versão 6.7.0.) in <b>/home/acasinha/public_html/wp-includes/functions.php</b> on line <b>6131</b><br />
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<b>Warning</b>:  Undefined variable $op in <b>/home/acasinha/public_html/wp-content/plugins/gt-tabs/index.php</b> on line <b>102</b><br />
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<b>Warning</b>:  Undefined array key "GTTabs" in <b>/home/acasinha/public_html/wp-content/plugins/gt-tabs/index.php</b> on line <b>184</b><br />
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<b>Warning</b>:  Undefined variable $op in <b>/home/acasinha/public_html/wp-content/plugins/gt-tabs/index.php</b> on line <b>102</b><br />
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<b>Warning</b>:  Undefined array key "GTTabs" in <b>/home/acasinha/public_html/wp-content/plugins/gt-tabs/index.php</b> on line <b>184</b><br />
{"id":23129,"date":"2022-11-18T17:38:44","date_gmt":"2022-11-18T17:38:44","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23129"},"modified":"2022-11-21T08:03:12","modified_gmt":"2022-11-21T08:03:12","slug":"23129","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23129","title":{"rendered":"Dois insetos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23129' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23129' class='GTTabs_curr'><a  id=\"23129_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23129' ><a  id=\"23129_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_23129'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5764\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5764\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14.jpg\" data-orig-size=\"431,425\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Insectos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14.jpg\" class=\"alignright wp-image-5764\" title=\"Insectos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14-300x295.jpg\" alt=\"\" width=\"240\" height=\"237\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14-300x295.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14-150x147.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14-400x394.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag25-14.jpg 431w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Um inseto parte do ponto M e percorre os segmentos [MA] e [AC], parando no ponto C.<\/p>\n<p>Um outro inseto parte do ponto C e percorre os segmentos [CB] e [BM], parando no ponto M.<\/p>\n<ol>\n<li>Prova que os tri\u00e2ngulos [AMC] e [CMB] s\u00e3o semelhantes.<\/li>\n<li>Determina:<br \/>&#8211; a dist\u00e2ncia que separa os dois insetos;<br \/>&#8211; a dist\u00e2ncia percorrida pelo primeiro inseto.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23129' onClick='GTTabs_show(1,23129)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23129'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><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\":690,\r\n\"height\":260,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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\"};\r\n\/\/ 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': 1,'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<ol>\n<li>Ambos os tri\u00e2ngulos possuem um \u00e2ngulo reto: \u00e2ngulos <span style=\"color: #ff0000;\">AMC<\/span> e <span style=\"color: #ff0000;\">BMC<\/span>.<br \/>Os \u00e2ngulos <span style=\"color: #0000ff;\">ACM<\/span> e <span style=\"color: #008000;\">MCB<\/span> s\u00e3o complementares, isto \u00e9, \\(A\\hat CM + M\\hat CB = {90^{\\rm{o}}}\\).<br \/>Os \u00e2ngulos <span style=\"color: #0000ff;\">ACM<\/span> e <span style=\"color: #008000;\">MAC<\/span> s\u00e3o tamb\u00e9m complementares, isto \u00e9, \\(A\\hat CM + M\\hat AC = {90^{\\rm{o}}}\\). (Porqu\u00ea?)<br \/>Logo, os \u00e2ngulos\u00a0\u00a0<span style=\"color: #008000;\">MAC<\/span> e <span style=\"color: #008000;\">MCB<\/span> s\u00e3o geometricamente iguais.<br \/>Portanto, os tri\u00e2ngulos [AMC] e [CMB] s\u00e3o semelhantes, pois possuem dois \u00e2ngulos geometricamente iguais, cada um a cada um.<br \/><br \/><\/li>\n<li>No final dos percursos, os insetos encontram-se, respetivamente, nos pontos C e M.<br \/>Logo, a dist\u00e2ncia que os separa \u00e9 \\(\\overline {MC} \\).<br \/>Como os tri\u00e2ngulos considerados s\u00e3o semelhantes, ent\u00e3o os comprimentos dos lados correspondentes s\u00e3o diretamente proporcionais. Isto \u00e9:<br \/>\\[\\frac{{\\overline {AM} }}{{\\overline {MC} }} = \\frac{{\\overline {MC} }}{{\\overline {MB} }} = \\frac{{\\overline {AC} }}{{\\overline {CB} }}\\]<br \/>Logo, usando as duas primeiras raz\u00f5es, temos:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{3,6}}{{\\overline {MC} }} = \\frac{{\\overline {MC} }}{{6,4}}}&amp;{ \\Leftrightarrow {\\rm{\\;}}}&amp;{\\overline {MC} \\times \\overline {MC} = 3,6 \\times 6,4{\\rm{\\;}}}\\\\{}&amp;{ \\Leftrightarrow {\\rm{\\;}}}&amp;{{{\\overline {MC} }^2} = 23,04{\\rm{\\;}}}\\\\{}&amp;{ \\Leftrightarrow {\\rm{\\;}}}&amp;{\\overline {MC} = 4,8{\\rm{\\;}}}\\end{array}\\]<br \/>No final do percurso, os insetos encontram-se a 4,8 dm de dist\u00e2ncia.<br \/><br \/>A dist\u00e2ncia percorrida pelo primeiro inseto \u00e9 \\(\\overline {MA} + \\overline {AC} \\).<br \/>Como os tri\u00e2ngulos [ACM] e [ACB] (o menor e o maior dos tri\u00e2ngulos) tamb\u00e9m s\u00e3o semelhantes, tem-se:<br \/>\\[\\frac{{\\overline {AC} }}{{\\overline {AB} }} = \\frac{{\\overline {MC} }}{{\\overline {CB} }} = \\frac{{\\overline {AM} }}{{\\overline {AC} }}\\]<br \/>Logo, usando a primeira e terceira raz\u00f5es, temos:<br \/>\\[\\begin{array}{*{20}{l}}{\\frac{{\\overline {AC} }}{{10}} = \\frac{{3,6}}{{\\overline {AC} }}}&amp;{ \\Leftrightarrow {\\rm{\\;}}}&amp;{{{\\overline {AC} }^2} = 36{\\rm{\\;}}}\\\\{}&amp;{ \\Leftrightarrow {\\rm{\\;}}}&amp;{\\overline {AC} = 6{\\rm{\\;}}}\\end{array}\\]<br \/>Logo, a dist\u00e2ncia percorrida pelo primeiro inseto foi<br \/>\\[\\overline {MA} + \\overline {AC} = 3,6 + 6 = 9,6{\\mkern 1mu} dm\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23129' onClick='GTTabs_show(0,23129)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um inseto parte do ponto M e percorre os segmentos [MA] e [AC], parando no ponto C. Um outro inseto parte do ponto C e percorre os segmentos [CB] e [BM],&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20664,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,149],"series":[],"class_list":["post-23129","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-semelhanca-de-triangulos"],"views":231,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/8V1Pag025-14_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23129","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=23129"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23129\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20664"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23129"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}