{"id":13231,"date":"2018-01-10T22:48:26","date_gmt":"2018-01-10T22:48:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13231"},"modified":"2022-01-16T23:11:39","modified_gmt":"2022-01-16T23:11:39","slug":"13231","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13231","title":{"rendered":"Duas circunfer\u00eancias"},"content":{"rendered":"<p><ul id='GTTabs_ul_13231' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13231' class='GTTabs_curr'><a  id=\"13231_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13231' ><a  id=\"13231_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_13231'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13232\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13232\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\" data-orig-size=\"340,270\" 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\u00eancias\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\" class=\"alignright wp-image-13232\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6-300x238.png\" alt=\"\" width=\"240\" height=\"191\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6-300x238.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png 340w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Na figura est\u00e3o representadas duas circunfer\u00eancias, respetivamente, de centros O e B, tr\u00eas di\u00e2metros, [AC], [BD] e [OF], e o raio [BE] paralelo a [AO].<\/p>\n<p>Justifica que:<\/p>\n<ol>\n<li>Os \u00e2ngulos AOB, COD e EBF s\u00e3o iguais.<\/li>\n<li>As cordas [AB], [CD] e [EF] s\u00e3o iguais.<\/li>\n<li>Os arcos AB, CD e EF s\u00e3o iguais.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13231' onClick='GTTabs_show(1,13231)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13231'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13232\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13232\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\" data-orig-size=\"340,270\" 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\u00eancias\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png\" class=\"alignright wp-image-13232\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6-300x238.png\" alt=\"\" width=\"240\" height=\"191\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6-300x238.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6.png 340w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Os \u00e2ngulos AOB e COD s\u00e3o iguais, pois s\u00e3o verticalmente opostos.<br \/>\nOs \u00e2ngulos EBF e AOB s\u00e3o iguais, pois s\u00e3o \u00e2ngulos correspondentes e as retas AC\u00a0 EB s\u00e3o paralelas.<br \/>\nLogo, os \u00e2ngulos AOB, COD e EBF s\u00e3o iguais.<br \/>\n\u00ad<\/li>\n<li>Na mesma circunfer\u00eancia ou em circunfer\u00eancias iguais, a \u00e2ngulos ao centro iguais correspondem cordas iguais.<br \/>\nLogo, as cordas [AB], [CD] e [EF] s\u00e3o iguais, pois s\u00e3o correspondentes aos \u00e2ngulos ao centro AOB, COD e EBF, que s\u00e3o iguais.<br \/>\n\u00ad<\/li>\n<li>Na mesma circunfer\u00eancia ou em circunfer\u00eancias iguais, a\u00a0\u00e2ngulos ao centro iguais correspondem arcos iguais.<br \/>\nLogo, os arcos AB, CD e EF s\u00e3o iguais, pois s\u00e3o correspondentes aos\u00a0\u00e2ngulos ao centro AOB, COD e EBF, que s\u00e3o iguais.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13231' onClick='GTTabs_show(0,13231)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura est\u00e3o representadas duas circunfer\u00eancias, respetivamente, de centros O e B, tr\u00eas di\u00e2metros, [AC], [BD] e [OF], e o raio [BE] paralelo a [AO]. Justifica que: Os \u00e2ngulos AOB, COD&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20443,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,457,188],"series":[],"class_list":["post-13231","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-arco-de-circunferencia","tag-circunferencia"],"views":1854,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag123-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13231","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=13231"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13231\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20443"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13231"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13231"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13231"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13231"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}