{"id":145617,"date":"2025-09-29T17:52:15","date_gmt":"2025-09-29T20:52:15","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=145617"},"modified":"2025-10-21T09:48:15","modified_gmt":"2025-10-21T12:48:15","slug":"poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/","title":{"rendered":"Pol\u00edgonos inscritos em uma circunfer\u00eancia: defini\u00e7\u00e3o e propriedades"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Um tema que recentemente vem sendo bastante explorado nos <span id=\"urn:enhancement-6d8cb944-6d66-4011-bf30-becd9fe70062\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/vestibular\">vestibulares<\/span>, envolvendo diversos conceitos de <span id=\"urn:enhancement-f89ea4ca-3a70-4bbc-8881-2ac73f108516\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geometria<\/span>, &eacute; a inscri&ccedil;&atilde;o de <span id=\"urn:local-annotation-562925\" class=\"textannotation disambiguated\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos-na-circunferencia\">pol&iacute;gonos na circunfer&ecirc;ncia<\/span>, principalmente <span id=\"urn:enhancement-98dd4dc7-a2f1-4df6-acae-446a4354c43c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares, por conta que envolvem problemas com simetria de figuras, al&eacute;m de rela&ccedil;&otilde;es entre figuras e problemas com ap&oacute;tema e calculo do lado das figuras.<p class=\"wp-block-paragraph\">Veja mais sobre o assunto no artigo do Estrat&eacute;gia Vestibulares.<\/p><p class=\"wp-block-paragraph\"><div class=\"cta-medio\" style=\"background-image: url(https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2024\/08\/curso-enem-1-estrategia-vestibulares-ctamedio.jpg);\"><h3>Pacote Enem TOP <\/h3> <p>Estude com o Estrat\u00e9gia Vestibulares<\/p><div class=\"cta-botao\"><a id=\"cta-medio\" href=\"https:\/\/vestibulares.estrategia.com\/curso\/enem-top\/\" target=\"_blank\" style=\"background:rgb(255,150,0)\">Saiba mais<\/a><\/div><\/div>\n\n\n\n<\/p><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Navegue pelo conte\u00fado<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/#Definicao-de-poligono-inscrito\" >Defini&ccedil;&atilde;o de pol&iacute;gono inscrito<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/#Poligonos-regulares-inscritos\" >Pol&iacute;gonos regulares inscritos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/#Propriedade-dos-principais-poligonos-regulares-inscritos\" >Propriedade dos principais pol&iacute;gonos regulares inscritos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/#Questoes-sobre-poligonos-inscritos\" >Quest&otilde;es sobre pol&iacute;gonos inscritos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-inscritos-em-uma-circunferencia-definicao-e-propriedades\/#Alcance-a-aprovacao-com-o-Estrategia-Vestibulares\" >Alcance a aprova&ccedil;&atilde;o com o Estrat&eacute;gia Vestibulares!<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-definicao-de-poligono-inscrito\"><span class=\"ez-toc-section\" id=\"Definicao-de-poligono-inscrito\"><\/span>Defini&ccedil;&atilde;o de pol&iacute;gono inscrito<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">De modo geral, definimos que um <span id=\"urn:enhancement-0c2c48ec-a1ab-492b-a90b-33bc61f694a7\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> est&aacute; inscrito em uma <span id=\"urn:enhancement-6acb46ab-a5d0-425a-bf7e-24a67d3f4c2c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> se todos os seus v&eacute;rtices pertencem &agrave; <span id=\"urn:enhancement-81514551-d210-43b5-8e38-64880567b36e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> que o envolve, como mostrado na figura a seguir. Assim, podemos afirmar que o <span id=\"urn:enhancement-5f3e7cba-e678-44b6-ae94-7a88a46b022b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> est&aacute; inscrito na <span id=\"urn:enhancement-e83f0f2e-c1f3-4284-97af-0ada58aa36be\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> e que a <span id=\"urn:enhancement-dd0e575a-dd4d-4707-ac49-c3a726159101\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncias<\/span> est&aacute; circunscrita ao <span id=\"urn:enhancement-554368db-7c31-4c4b-9ff0-0bc89457dcab\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>.<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"1024\" height=\"329\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-67-1.jpg\" alt=\"\" class=\"wp-image-145645\" style=\"width:470px;height:auto\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-67-1.jpg 1024w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-67-1-768x247.jpg 768w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-67-1-800x257.jpg 800w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><p class=\"wp-block-paragraph\">No dia a dia, diversas constru&ccedil;&otilde;es arquitet&ocirc;nicas e designers utilizam da circunscri&ccedil;&atilde;o, como para montar c&uacute;pulas e elementos das catedrais, al&eacute;m das constru&ccedil;&otilde;es <span id=\"urn:enhancement-e924d0b8-3046-4dc6-b33c-768c9256ea85\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;tricas<\/span>, a circunscri&ccedil;&atilde;o tem variadas aplica&ccedil;&otilde;es trigonom&eacute;tricas.<\/p><h2 class=\"wp-block-heading\" id=\"h-poligonos-regulares-inscritos\"><span class=\"ez-toc-section\" id=\"Poligonos-regulares-inscritos\"><\/span>Pol&iacute;gonos regulares inscritos<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">A import&acirc;ncia dos <span id=\"urn:enhancement-c14ea45b-1f42-4ddd-a9c6-24cdfcfd5b89\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares &eacute; que eles apresentam propriedades que realmente simplificam os c&aacute;lculos. Nesse tipo de <span id=\"urn:enhancement-2d1906de-fa1b-4db1-8151-046196e7b113\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span>, todos os lados e &acirc;ngulos internos s&atilde;o congruentes, com tal simetria, mesmo tendo apenas a medida de um lado &eacute; poss&iacute;vel achar a &aacute;rea, ap&oacute;tema, &acirc;ngulos internos, etc.<\/p><p class=\"wp-block-paragraph\">Outra vantagem desse tipo de figura &eacute; que elas podem ser decompostas em <span id=\"urn:enhancement-dcce67a6-cd04-4cf6-b080-6aa34e69b1b5\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span> is&oacute;sceles id&ecirc;nticos, transformando um problema complexo em um simples e &aacute;rea de <span id=\"urn:enhancement-20123f00-2656-41f7-b095-da8ecd0383d4\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span>. Os raios da <span id=\"urn:enhancement-44d38f3d-0e8a-4cc5-9bfe-32f597732ed3\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> que ligam os v&eacute;rtices do <span id=\"urn:enhancement-09265aff-4f0b-4ce7-b1fa-905b64a6fd10\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> inscritos ao centro dele s&atilde;o os lados do <span id=\"urn:enhancement-f1fe95c6-3b95-4fa1-9239-9801f08a9286\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span>.<\/p><p class=\"wp-block-paragraph\">Um conceito muito utilizado &eacute; o ap&oacute;tema, ele pode ser definido como um segmento de reta especial que parte do centro de um <span id=\"urn:enhancement-707ffdce-cabd-43d7-b8fd-b891775ca34d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> regular e alcan&ccedil;a o ponto m&eacute;dio de um de seus lados, sempre formando um <span id=\"urn:enhancement-0dbd8f29-9859-4e85-bd12-fe39b464a27c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/angulos-retos\">&acirc;ngulo reto<\/span> com esse lado, ou seja, sendo perpendicular a ele.<\/p><p class=\"wp-block-paragraph\">H&aacute;, ainda, o conceito de circuncentro da figura, que &eacute; o ponto central da <span id=\"urn:enhancement-aa5edc11-999a-45a9-a024-92475feae1fc\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita, que coincide com o centro dos <span id=\"urn:enhancement-e9ebf580-9fc8-424f-9613-febb394b9aff\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares inscritos. Do centro, saindo dois raios vizinhos at&eacute; o v&eacute;rtice, temos o &acirc;ngulo central do <span id=\"urn:enhancement-b23d736a-23c1-4da2-952b-ddf5069374ac\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>, que &eacute; constante =360&deg;\/n.<\/p><h2 class=\"wp-block-heading\" id=\"h-propriedade-dos-principais-poligonos-regulares-inscritos\"><span class=\"ez-toc-section\" id=\"Propriedade-dos-principais-poligonos-regulares-inscritos\"><\/span>Propriedade dos principais pol&iacute;gonos regulares inscritos<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-triangulo-equilatero\">Tri&acirc;ngulo equil&aacute;tero<\/h3><p class=\"wp-block-paragraph\">Dado um <span id=\"urn:enhancement-8d86cc98-2b1d-4a23-998f-e0abe7164144\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero, com os tr&ecirc;s lados de mesma medida, inscrito em uma <span id=\"urn:enhancement-860aeeaa-c0dd-4fdf-81b5-92262a2393dd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> de<strong> <span id=\"urn:enhancement-807f3dbb-05bd-4770-ab29-86f436994959\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/raio\">raio<\/span> R<\/strong>.<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"210\" height=\"214\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-52.png\" alt=\"\" class=\"wp-image-145625\"><\/figure><p class=\"wp-block-paragraph\">O lado L &eacute; dado por<em> L=R&radic;3<\/em>, portanto o per&iacute;metro ser&aacute; o triplo disso (<em>P=3L=3R&radic;3<\/em>). A altura &eacute; <em>h=3R\/2<\/em>, o ap&oacute;tema &eacute;<em> a=R\/2<\/em>, porque o centro do <span id=\"urn:enhancement-74a6c0cd-b3f7-403a-b3cd-1040c28d9fbf\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero divide a altura na raz&atilde;o 2:1. Como a altura &eacute; <em>h=3R\/2<\/em>, a <span id=\"urn:enhancement-f2e09e0d-5b33-458e-89f5-5892f0eeab90\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> do centro ao lado (ap&oacute;tema) &eacute; &#8531; da altura.<\/p><p class=\"wp-block-paragraph\">Com os valores dos lados, encontramos a &aacute;rea pela seguinte rela&ccedil;&atilde;o:&nbsp;<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"363\" height=\"29\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-53.png\" alt=\"\" class=\"wp-image-145626\"><\/figure><h3 class=\"wp-block-heading\" id=\"h-quadrado\">Quadrado<\/h3><p class=\"wp-block-paragraph\">A diagonal do quadrado &eacute; exatamente <em>d=2R<\/em>, enquanto o lado vai ser <em>L=R&radic;2<\/em>, sendo o per&iacute;metro&nbsp; <em>P=4L=4R&radic;2<\/em>, pois: <\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"462\" height=\"34\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-54.png\" alt=\"\" class=\"wp-image-145627\"><\/figure><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"257\" height=\"193\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-50.png\" alt=\"\" class=\"wp-image-145623\"><\/figure><p class=\"wp-block-paragraph\">A per&iacute;metro ser&aacute; P=4L=4R&radic;2 e o ap&oacute;tema, sendo a <span id=\"urn:enhancement-50faedc7-c041-40b8-b90e-41eb5b93a40a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> do centro do quadrado at&eacute; um dos lados, vai ser metade do lado <em>a=L\/2=(R&radic;2)\/2<\/em>. Sua &aacute;rea vai ser <\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"160\" height=\"39\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-56.png\" alt=\"\" class=\"wp-image-145629\"><\/figure><h3 class=\"wp-block-heading\" id=\"h-hexagono\">Hex&aacute;gono<\/h3><p class=\"wp-block-paragraph\">O hex&aacute;gono regular vai apresentar o lado L igual ao <span id=\"urn:enhancement-9db858d3-ca07-4a91-97ad-432d0ea1a190\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/raio\">raio<\/span> (<em>L=R<\/em>), isso ocorre por conta que o hex&aacute;gono pode ser dividido em 6 <span id=\"urn:enhancement-9334135f-0486-4443-950d-6aff8af4152b\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span> equil&aacute;teros congruentes, com isso o <span id=\"urn:enhancement-becbf86b-8bf6-42e3-a0f5-20776c36cfde\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/raio\">raio<\/span> coincide com o tamanho L.<\/p><p class=\"wp-block-paragraph\">O per&iacute;metro vai ser <em>P=6L=6R<\/em>, enquanto o ap&oacute;tema vai ser a altura de um dos <span id=\"urn:enhancement-6b39dae0-d063-4c48-8934-3a13d31d9c60\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span> equil&aacute;teros que formam o hex&aacute;gono<em> a = (R&radic;3)\/2<\/em> e a &aacute;rea: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"659\" height=\"546\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-67.jpg\" alt=\"\" class=\"wp-image-145644\" style=\"width:291px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Conforme mostra a figura, temos um hex&aacute;gono inscrito e &eacute; poss&iacute;vel dividi-lo em 6 <span id=\"urn:enhancement-a8e4cac9-5ccb-4f35-bcc6-c0eb8259c128\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span> equil&aacute;teros. A partir de um desses <span id=\"urn:enhancement-38a31e29-639c-4a31-931d-a8ea322ace81\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulos<\/span> e usando o <span id=\"urn:enhancement-834dfbb9-e712-43d8-b13f-b9eacb466f99\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/teorema-de-pitagoras\">teorema de Pit&aacute;goras<\/span> &eacute; not&aacute;vel a rela&ccedil;&atilde;o entre o <span id=\"urn:enhancement-5224d8de-3bd0-4915-9f8b-a0c610e08a87\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/raio\">raio<\/span>, metade do lado e o ap&oacute;tema: R2=l2\/4+a2 .<\/p><p class=\"wp-block-paragraph\">Usando a simetria, sabemos que o &acirc;ngulo central no hex&aacute;gono vai ser 60&deg;, pois<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"138\" height=\"25\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-59.png\" alt=\"\" class=\"wp-image-145632\"><\/figure><p class=\"wp-block-paragraph\">O novo &acirc;ngulo formado pr&oacute;ximo ao centro O do tri&acirc;ngulo ret&acirc;ngulo formado ser&aacute; metade do &acirc;ngulo central:<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"113\" height=\"26\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-58.png\" alt=\"\" class=\"wp-image-145631\"><\/figure><p class=\"wp-block-paragraph\"><\/p><h3 class=\"wp-block-heading\" id=\"h-poligonos-nao-regulares\">Pol&iacute;gonos n&atilde;o regulares<\/h3><p class=\"wp-block-paragraph\">Os <strong><span id=\"urn:enhancement-863548f6-3e72-4192-bfb9-6509ab75375a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> n&atilde;o regulares inscritos<\/strong> s&atilde;o figuras geom&eacute;tricas que possuem todos os seus v&eacute;rtices localizados exatamente sobre uma mesma <span id=\"urn:enhancement-167df906-f8c4-4be7-8873-5143fba57869\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. A principal caracter&iacute;stica que os diferencia dos <span id=\"urn:enhancement-6a006895-5ea4-4ab9-b6f1-873f5f425e0e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares &eacute; que, apesar de estarem todos dentro de um <span id=\"urn:enhancement-1f8bed11-2537-44bc-ba22-d36187e8efde\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span>, eles n&atilde;o apresentam lados com o mesmo comprimento nem &acirc;ngulos internos iguais entre si. Isso significa que suas medidas podem variar bastante, mesmo que todos os v&eacute;rtices estejam distribu&iacute;dos sobre a borda do <span id=\"urn:enhancement-cc899604-1e73-40cd-a9c2-c064442093c4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span>.<\/p><p class=\"wp-block-paragraph\">Para que um <span id=\"urn:enhancement-a87b3672-d325-4ee1-acdf-f3c147895523\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> seja considerado <strong>inscrit&iacute;vel<\/strong>, ou seja, possa ser constru&iacute;do dentro de uma <span id=\"urn:enhancement-c919b2c9-f397-422b-becd-366ed091288b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>, a &uacute;nica exig&ecirc;ncia &eacute; que todos os seus v&eacute;rtices toquem a <span id=\"urn:enhancement-cd8f579b-b282-4f01-afda-23c491977c2f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Assim, n&atilde;o h&aacute; necessidade de que o <span id=\"urn:enhancement-14541fe5-f73f-47c2-90ce-7a81859f14a0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> seja regular, bastando apenas que essa condi&ccedil;&atilde;o seja satisfeita.<\/p><p class=\"wp-block-paragraph\"><span id=\"urn:enhancement-a3f1fa84-2d61-4d5c-84ed-914d16dc2412\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">Tri&acirc;ngulos<\/span> escalenos e <span id=\"urn:enhancement-c9b62773-c344-4771-8ec0-f3d7d849f546\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/retangulo\">ret&acirc;ngulos<\/span> s&atilde;o &oacute;timos exemplos, e para resolver problemas que envolvem este tipo de figura n&atilde;o apresenta uma f&oacute;rmula a ser seguida por conta da falta de simetria. Em suma, utilizam a Lei dos Senos e Cossenos, ou outras propriedades espec&iacute;ficas para resolver este tipo de problema.&nbsp;<\/p><h2 class=\"wp-block-heading\" id=\"h-questoes-sobre-poligonos-inscritos\"><span class=\"ez-toc-section\" id=\"Questoes-sobre-poligonos-inscritos\"><\/span>Quest&otilde;es sobre pol&iacute;gonos inscritos<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-centro-universitario-sao-lucas-2018\">Centro Universit&aacute;rio S&atilde;o Lucas (2018)<\/h3><p class=\"wp-block-paragraph\">Sobre <span id=\"urn:enhancement-b35294c5-211d-4999-9f82-cc05e6dcf84f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares, marque V para as afirmativas verdadeiras e F para as falsas.<\/p><p class=\"wp-block-paragraph\">( &nbsp; ) O ap&oacute;tema de um <span id=\"urn:enhancement-39fc125c-294d-471d-8194-d4897ba50cc4\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero inscrito &eacute; ap&#8323; = R\/2.<\/p><p class=\"wp-block-paragraph\">( &nbsp; ) O ap&oacute;tema de um quadrado circunscrito &eacute; ap&#8324; = R.<\/p><p class=\"wp-block-paragraph\">( &nbsp; ) O ap&oacute;tema de um hex&aacute;gono circunscrito &eacute; ap&#8326; = R.<\/p><p class=\"wp-block-paragraph\">( &nbsp; ) O ap&oacute;tema de um <span id=\"urn:enhancement-19d8913a-6f27-45b3-bea2-242ccc0fed28\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero circunscrito &eacute; ap&#8323; = R&radic;3<\/p><p class=\"wp-block-paragraph\">A <span id=\"urn:enhancement-c86bf45d-dcaa-4fd8-bdb7-b7be65ac9c67\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/sequencias-numericas\">sequ&ecirc;ncia<\/span> est&aacute; correta em<\/p><p class=\"wp-block-paragraph\"><strong>A)<\/strong> V, V, V, V<br><strong>B)<\/strong> V, F, V, V<br><strong>C)<\/strong> F, F, V, V<br><strong>D)<\/strong> V, V, V, F<\/p><p class=\"wp-block-paragraph\"><\/p><details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary><strong>Resposta<\/strong><\/summary>\n<p class=\"wp-block-paragraph\">Alternativa correta: <strong>D<\/strong><\/p>\n<\/details><p class=\"wp-block-paragraph\"><\/p><h2 class=\"wp-block-heading\" id=\"h-alcance-a-aprovacao-com-o-estrategia-vestibulares\"><span class=\"ez-toc-section\" id=\"Alcance-a-aprovacao-com-o-Estrategia-Vestibulares\"><\/span>Alcance a aprova&ccedil;&atilde;o com o Estrat&eacute;gia Vestibulares!<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Aqui no EV, voc&ecirc; encontra os melhores e mais completos conte&uacute;dos selecionados com os assuntos mais cobrados nos <span id=\"urn:enhancement-8a434019-c671-4b9a-8852-832ad462825b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/vestibular\">vestibulares<\/span>. Escolha o <span id=\"urn:enhancement-311d37fb-d610-4930-b408-dc8a5bfb1fed\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano\">plano<\/span> ideal para suas metas e foque nas &aacute;reas que mais precisa para conquistar o curso dos seus sonhos.<\/p><p class=\"wp-block-paragraph\">Clique no banner e comece agora mesmo!<\/p><p class=\"wp-block-paragraph\"><a id=\"cta\" class=\"cta-imagem\" href=\"https:\/\/vestibulares.estrategia.com\/cursos\/\" target=\"blank\">\n                <img decoding=\"async\" width=\"100%\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2021\/12\/EV4.jpg\" alt=\"CTA - Estrat\u00e9gia Vestibulares 4\" title=\"CTA - Estrat\u00e9gia Vestibulares 4\">\n        <\/a>\n\n\n<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"Entenda mais sobre as defini\u00e7\u00f5es, propriedades e aplica\u00e7\u00f5es de pol\u00edgonos inscritos dentro de circunfer\u00eancias\n","protected":false},"author":61,"featured_media":145652,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-145617","post","type-post","status-publish","format-standard","has-post-thumbnail","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.9 (Yoast SEO v28.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Pol\u00edgonos inscritos em uma circunfer\u00eancia: defini\u00e7\u00e3o e propriedades<\/title>\n<meta name=\"description\" content=\"Entenda mais sobre as defini\u00e7\u00f5es, propriedades e aplica\u00e7\u00f5es de pol\u00edgonos inscritos dentro de circunfer\u00eancias.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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