\nEnunciado<\/b><\/span><\/p>\n
$\"\"$ <\/a>Na figura est\u00e1 representada uma circunfer\u00eancia.<\/p>\n
Sabe-se que:<\/p>\n
\n
[AC] \u00e9 um di\u00e2metro de comprimento 15;<\/li>\n
B \u00e9 um ponto da circunfer\u00eancia.<\/li>\n
\$\\overline {AB} = 12\$<\/li>\n<\/ul>\n
\n
Justifica que o tri\u00e2ngulo [ABC] \u00e9 ret\u00e2ngulo em B.<\/li>\n
Calcula a \u00e1rea da regi\u00e3o sombreada a laranja na figura.
\nApresenta os c\u00e1lculos que efetuares e, na tua resposta, escreve o resultado arredondado \u00e0s unidades.<\/li>\n<\/ol>\n
Resolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n
\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
\n
\n
\n
$\"\"$ <\/a>[AC] \u00e9 um di\u00e2metro de comprimento 15;<\/p>\n<\/blockquote>\n<\/li>\n
\n
\n
B \u00e9 um ponto da circunfer\u00eancia.<\/p>\n<\/blockquote>\n<\/li>\n
\n
\n
\$\\overline {AB} = 12\$<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n
\n
Como [AC] \u00e9 um di\u00e2metro, ent\u00e3o o \u00e2ngulo ABC est\u00e1 escrito num arco de semicircunfer\u00eancia. Consequentemente, este \u00e2ngulo \u00e9 ret\u00e2ngulo, pois \$A\\widehat BC = \\frac{{\\overparen{AC}}}{2} = \\frac{{180^\\circ }}{2} = 90^\\circ \$.
\n\u00ad<\/li>\n
Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [ABC], temos:
\n\\[\\overline {BC} = \\sqrt {{{\\overline {AC} }^2} – {{\\overline {AB} }^2}} = \\sqrt {{{15}^2} – {{12}^2}} = \\sqrt {81} = 9\\]
\nPortanto, a \u00e1rea (em u.a.) da regi\u00e3o sombreada a laranja na figura \u00e9:
\n\\[\\begin{array}{*{20}{l}}{{A_{Sombreada}}}& = &{{A_\\bigcirc } – {A_{\\left[ {ABC} \\right]}}}\\\\{}& = &{\\pi \\times {{\\left( {{\\textstyle{{15} \\over 2}}} \\right)}^2} – \\frac{{12 \\times 9}}{2}}\\\\{}& = &{\\frac{{225\\pi – 216}}{4}}\\\\{}& \\approx &{123}\\end{array}\\]<\/li>\n<\/ol>\n
<< Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"
Enunciado Resolu\u00e7\u00e3o Enunciado Na figura est\u00e1 representada uma circunfer\u00eancia. Sabe-se que: [AC] \u00e9 um di\u00e2metro de comprimento 15; B \u00e9 um ponto da circunfer\u00eancia. \$\\overline {AB} = 12\$ Justifica que o tri\u00e2ngulo [ABC] \u00e9...<\/p>\n","protected":false},"author":1,"featured_media":20504,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,280,188],"series":[],"class_list":["post-13461","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-angulo-inscrito","tag-circunferencia"],"views":2846,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag149-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13461","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=13461"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13461\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20504"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13461"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}