{"id":145709,"date":"2025-09-30T12:34:19","date_gmt":"2025-09-30T15:34:19","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=145709"},"modified":"2025-10-08T15:53:19","modified_gmt":"2025-10-08T18:53:19","slug":"poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/","title":{"rendered":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es"},"content":{"rendered":"<p class=\"wp-block-paragraph\">A mat&eacute;ria sobre <span id=\"urn:enhancement-15ef095d-625c-46d0-ad49-56f7b02ebf28\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> &eacute; uma daquelas que sempre chamam a aten&ccedil;&atilde;o em provas de vestibulares e olimp&iacute;adas de <span id=\"urn:enhancement-773d1262-2823-4c04-a48d-11ee51b7e77c\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/matematica\">matem&aacute;tica<\/span>. Isso porque ela re&uacute;ne v&aacute;rias propriedades importantes da <span id=\"urn:enhancement-662d7aa7-d2ea-4aa1-9d8c-934755a38f54\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geometria<\/span>, como <span id=\"urn:local-annotation-696177\" class=\"textannotation disambiguated\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/angulo\">&acirc;ngulos<\/span>, &aacute;reas e inscritos, rela&ccedil;&otilde;es entre cordas e ap&oacute;temas, al&eacute;m de no&ccedil;&otilde;es de simetria e regularidade.<p class=\"wp-block-paragraph\">Para entender como essas figuras funcionam e se relacionam com a <span id=\"urn:enhancement-c5f021b2-1bbb-404c-ab17-130070eeaf98\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geometria<\/span>, leia mais sobre <span id=\"urn:local-annotation-487145\" class=\"textannotation disambiguated\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos-circunscritos-na-circunferencia\">Pol&iacute;gonos Circunscritos na Circunfer&ecirc;ncia<\/span> no artigo a seguir 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-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#O-que-e-um-poligono-circunscrito-na-Circunferencia\" >O que &eacute; um pol&iacute;gono circunscrito na Circunfer&ecirc;ncia<\/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-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Poligonos-regulares\" >Pol&iacute;gonos regulares<\/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-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Elementos-importantes-do-poligono-regular-circunscrito\" >Elementos importantes do pol&iacute;gono regular circunscrito<\/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-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Formulas-e-propriedades-dos-principais-poligonos-regulares-circunscritos\" >F&oacute;rmulas e propriedades dos principais pol&iacute;gonos regulares circunscritos<\/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-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Perimetro-e-Area-de-Poligonos-Regulares-Circunscritos-O-perimetro-de-um-poligono-regular-e-bem-tranquilo-de-calcular-basta-multiplicar-o-numero-de-lados-N-pelo-comprimento-de-um-lado-ln%E2%80%8B-ou-seja\" >Per&iacute;metro e &Aacute;rea de Pol&iacute;gonos Regulares Circunscritos: O per&iacute;metro de um pol&iacute;gono regular &eacute; bem tranquilo de calcular, basta multiplicar o n&uacute;mero de lados N pelo comprimento de um lado ln&#8203;, ou seja,<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Poligonos-Inscritos-X-Poligonos-Circunscritos\" >Pol&iacute;gonos Inscritos X Pol&iacute;gonos Circunscritos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#Questoes-sobre-poligonos-circunscritos\" >Quest&otilde;es sobre pol&iacute;gonos circunscritos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#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-o-que-e-um-poligono-circunscrito-na-circunferencia\"><span class=\"ez-toc-section\" id=\"O-que-e-um-poligono-circunscrito-na-Circunferencia\"><\/span>O que &eacute; um pol&iacute;gono circunscrito na Circunfer&ecirc;ncia<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Os pol&iacute;gonos circunscritos na circunfer&ecirc;ncia s&atilde;o uma categoria de figuras geom&eacute;tricas planas onde o pol&iacute;gono est&aacute; situado ao redor de uma circunfer&ecirc;ncia, de modo que cada um dos seus lados toca a circunfer&ecirc;ncia em um &uacute;nico ponto, sendo, portanto, tangente a ela. Esta circunfer&ecirc;ncia, que est&aacute; contida no interior do pol&iacute;gono e &eacute; tocada por todos os seus lados, &eacute; denominada circunfer&ecirc;ncia inscrita.<\/p><p class=\"wp-block-paragraph\">Um <span id=\"urn:enhancement-bcbcb63a-9e5c-4be7-9ceb-7a90f088816c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> estar circunscrito a uma <span id=\"urn:enhancement-6ed15539-4701-4d71-a9aa-a7386dfa15cd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> significa que todos os seus lados s&atilde;o tangentes a essa <span id=\"urn:enhancement-c1a3a3f7-12b4-400f-83ed-9713a334a4b1\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>, ou seja, cada lado do <span id=\"urn:enhancement-4e73b96b-f116-4e14-9caf-99f968406482\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> toca a <span id=\"urn:enhancement-1215b5f2-91e4-4bab-9bd8-0ffd5dee02ac\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> em apenas um ponto, sem atravess&aacute;-la. J&aacute; a <span id=\"urn:enhancement-57b5434d-fd20-42c0-8159-0bea660dcc80\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> que est&aacute; dentro do <span id=\"urn:enhancement-467f3bb7-b8af-45d0-80e7-04d46fd2b263\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>, que &eacute; tangenciada por todos os seus lados, &eacute; chamada de <span id=\"urn:enhancement-b2ca01e3-a09d-49c1-ba7b-b07c229dbcbb\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita no <span id=\"urn:enhancement-270d6c70-136a-467f-b9d6-42552dd939a4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>.&nbsp;<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"606\" height=\"162\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-79.png\" alt=\"\" class=\"wp-image-145716\"><\/figure><p class=\"wp-block-paragraph\">Essa configura&ccedil;&atilde;o <span id=\"urn:enhancement-c11ccf67-3549-4b5f-8971-682de04f3393\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;trica<\/span> &eacute; caracter&iacute;stica dos <span id=\"urn:enhancement-c5e15177-ea01-4293-80d3-45ebdbb405fb\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> circunscritos e possui importantes propriedades, especialmente em <span id=\"urn:enhancement-0e071ed7-72c4-4b53-a7ec-e861e1e47979\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares, onde todos os lados s&atilde;o iguais e a <span id=\"urn:enhancement-031ee32d-4416-4be8-be82-cd9954a2f5b7\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita &eacute; perfeitamente centralizada.<\/p><h2 class=\"wp-block-heading\" id=\"h-poligonos-regulares\"><span class=\"ez-toc-section\" id=\"Poligonos-regulares\"><\/span><br>Pol&iacute;gonos regulares<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Quando o <span id=\"urn:enhancement-0439ed24-384c-430a-83bc-ebda5a24cc6a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> &eacute; <strong>regular<\/strong> algumas propriedades <span id=\"urn:enhancement-68bbe5e9-ad35-445e-a1a7-b3b80171202a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;tricas<\/span> se destacam. Uma delas &eacute; a exist&ecirc;ncia de um <strong>centro do <span id=\"urn:enhancement-8b37740e-dfee-4a18-951b-cc8e6fdd6ccd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span><\/strong>, que &eacute; um ponto &uacute;nico que se localiza &agrave; mesma <span id=\"urn:enhancement-0afd3c32-03b8-4ef1-8a14-c5498a5d97cf\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> de todos os v&eacute;rtices e &agrave; mesma <span id=\"urn:enhancement-cedd7ad3-e4fc-4aef-b48a-a0ec25a47071\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> de todos os lados.&nbsp;<\/p><p class=\"wp-block-paragraph\">Outra propriedade &eacute; a <strong><span id=\"urn:enhancement-d90a849b-cff3-4d61-8e0d-6415981518a0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita<\/strong>, trata-se da <span id=\"urn:enhancement-2f96a4e0-623b-4596-b6a3-d329be54dcfb\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> que passa exatamente por todos os v&eacute;rtices do <span id=\"urn:enhancement-679b2144-88bd-463a-85ce-252542b36962\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> regular. O centro dessa <span id=\"urn:enhancement-19b68a54-a79c-4b3f-92a9-b0f50334f37d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> coincide com o centro do <span id=\"urn:enhancement-5377e514-8760-4e32-9e5e-9eb637002d9b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>, refor&ccedil;ando a ideia de equil&iacute;brio e uniformidade da figura.<\/p><p class=\"wp-block-paragraph\">Al&eacute;m disso, o <span id=\"urn:enhancement-8fc3fc2f-194e-4f50-ace1-f64953c6ed6f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> regular tamb&eacute;m possui <strong><span id=\"urn:enhancement-ca42a82c-0b04-4460-a6dc-ce7ca2d5dc50\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita<\/strong>, ou seja, uma <span id=\"urn:enhancement-23518a2d-00b2-49c2-a62f-5fc3d1c14e5b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> que toca todos os lados do <span id=\"urn:enhancement-d248201a-92bd-4ccc-865a-0259b317f114\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> em um &uacute;nico ponto de cada lado. Assim como a <span id=\"urn:enhancement-3d2cf718-cf71-4355-b98d-95d3b309b423\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita, o centro da <span id=\"urn:enhancement-6c24786d-413f-42a0-a99c-16f3f354c2e0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita coincide com o centro do <span id=\"urn:enhancement-7166e195-8564-44b3-a341-301cdd5b5a8b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>, mostrando que esse ponto central &eacute; realmente respons&aacute;vel por unificar todas as suas propriedades <span id=\"urn:enhancement-4e93fcb2-09d8-443b-8ef3-3179013cd453\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;tricas<\/span>.<\/p><p class=\"wp-block-paragraph\">Os <strong>centros coincidem<\/strong> devido &agrave; simetria rotacional, o ponto equidistante de todos os v&eacute;rtices (centro da <span id=\"urn:enhancement-78dcad69-527c-4076-bac6-d46368e13e24\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita) &eacute; tamb&eacute;m equidistante de todos os lados (centro da <span id=\"urn:enhancement-4250da9a-d4f1-477d-b4a7-7d46a66a00b0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita).&nbsp;<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"394\" height=\"246\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-80.png\" alt=\"\" class=\"wp-image-145717\"><\/figure><p class=\"wp-block-paragraph\">Geometricamente, esse ponto pode ser visto como a interse&ccedil;&atilde;o entre todas as bissetrizes dos &acirc;ngulos internos e tamb&eacute;m entre todas as mediatrizes dos lados, mostrando que ele ocupa uma posi&ccedil;&atilde;o central na figura.<\/p><h2 class=\"wp-block-heading\" id=\"h-elementos-importantes-do-poligono-regular-circunscrito\"><span class=\"ez-toc-section\" id=\"Elementos-importantes-do-poligono-regular-circunscrito\"><\/span>Elementos importantes do pol&iacute;gono regular circunscrito<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Em<strong> <span id=\"urn:enhancement-de8bf29a-5d83-43fc-b62a-f37bdc2894cd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares circunscritos a uma <span id=\"urn:enhancement-3a1ca67d-be3c-4622-bfe4-199ac39b1721\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span><\/strong>, o comprimento do ap&oacute;tema (a&#8345;) e o raio (r) da <span id=\"urn:enhancement-36168c50-18ad-4211-974d-c2f006665003\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita s&atilde;o numericamente iguais. Para melhor compreens&atilde;o vamos definir ambos os conceitos.<\/p><p class=\"wp-block-paragraph\">O ap&oacute;tema &eacute; o segmento que vai do centro da figura at&eacute; o ponto m&eacute;dio de um lado, formando 90&deg; com ele. J&aacute; o raio do inc&iacute;rculo &eacute; o segmento de reta que vai do centro do <span id=\"urn:enhancement-6f38a848-1e6c-4d67-bb1a-a07b20aa3f5e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> at&eacute; o ponto de tang&ecirc;ncia com um lado, formando 90&deg; com ele.<\/p><p class=\"wp-block-paragraph\">Em um <span id=\"urn:enhancement-c1807280-f433-471c-9d30-ffc021b3b925\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> regular, a simetria garante que o ponto de tang&ecirc;ncia do inc&iacute;rculo com um lado seja exatamente o ponto m&eacute;dio desse lado. Assim, o segmento de reta que &eacute; o raio, tamb&eacute;m seja o ap&oacute;tema. Tal segmento &eacute; muito importante, pois aparece em c&aacute;lculos de &aacute;rea e em rela&ccedil;&otilde;es m&eacute;tricas.<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"262\" height=\"207\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-81.png\" alt=\"\" class=\"wp-image-145718\"><\/figure><p class=\"wp-block-paragraph\">Outro elemento &eacute; o <strong>lado do <span id=\"urn:enhancement-0eaca1ea-f024-4f98-af5b-90f62954b8f7\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> (l&#8345;)<\/strong>, que representa a medida de cada um dos lado do <span id=\"urn:enhancement-5e81512c-5cc8-4282-9986-962499fba71f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> de N lados iguais. Enquanto que, o <strong>raio da <span id=\"urn:enhancement-43bd5bfc-e8fd-49f2-9c6f-5702432940f5\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita (R)<\/strong> &eacute; a <span id=\"urn:enhancement-04b0ef20-1f42-4462-8415-ddacb5face66\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> do centro do <span id=\"urn:enhancement-6a5d8b37-a1e2-414d-95ad-81ad7e4ee04d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> at&eacute; qualquer v&eacute;rtice, ou seja, o segmento de reta que conecta o centro a um dos v&eacute;rtices.<\/p><p class=\"wp-block-paragraph\">Esses elementos se relacionam diretamente, como ao observar metade de um lado do <span id=\"urn:enhancement-24918e39-633a-4b7e-b54b-d578352806d2\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span>, percebe-se que se <span id=\"urn:enhancement-b8092a21-8880-4c9f-93ed-0849d15e4761\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> um <strong>tri&acirc;ngulo ret&acirc;ngulo<\/strong> em que a <span id=\"urn:enhancement-4c5d584e-3c0f-4706-89cb-22abe56ef860\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/hipotenusa\">hipotenusa<\/span> &eacute; R, um <span id=\"urn:enhancement-590dcdf7-8a36-4329-86b1-b69491c73e86\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/cateto\">cateto<\/span> &eacute; o ap&oacute;tema r, e o outro <span id=\"urn:enhancement-c29285af-5e28-4152-9ab9-ee4837be996d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/cateto\">cateto<\/span> &eacute; <strong>l&#8345;<\/strong>\/2. Essa rela&ccedil;&atilde;o <span id=\"urn:enhancement-611ae23f-61e6-46a4-9b90-30000a71ea04\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;trica<\/span> &eacute; a base para diversas f&oacute;rmulas envolvendo <span id=\"urn:enhancement-4b08aecb-6f1b-4135-866f-948bcb28dba3\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares, permitindo calcular lados, raios e &aacute;reas de <span id=\"urn:enhancement-fb78b39a-7dde-40b1-b123-f71b27d7be33\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> mais pr&aacute;tica.<\/p><h2 class=\"wp-block-heading\" id=\"h-formulas-e-propriedades-dos-principais-poligonos-regulares-circunscritos\"><span class=\"ez-toc-section\" id=\"Formulas-e-propriedades-dos-principais-poligonos-regulares-circunscritos\"><\/span>F&oacute;rmulas e propriedades dos principais pol&iacute;gonos regulares circunscritos<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\">O <span id=\"urn:enhancement-04274c2b-f2ea-4244-9d50-5f24a3d8c989\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> circunscrito a uma <span id=\"urn:enhancement-4edfa643-0929-41ca-b036-695ebe8a86c7\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> est&aacute; fora do <span id=\"urn:enhancement-f2c5519f-665c-46ac-908e-7950f49e69ad\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span> com seus tr&ecirc;s lados tangenciando a <span id=\"urn:enhancement-fc2556ff-9faf-4683-a34c-b35e96b56037\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>.&nbsp;<\/p><p class=\"wp-block-paragraph\">Sabendo que a altura de um <span id=\"urn:enhancement-ec2dbfa7-bb6a-483d-8675-de608405a340\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero &eacute; <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"136\" height=\"75\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-82.png\" alt=\"\" class=\"wp-image-145719\" style=\"width:91px;height:auto\"><\/figure><p class=\"wp-block-paragraph\"> o raio vai ser r = h\/3. Substituindo vamos ter:<\/p><p class=\"wp-block-paragraph\">Lado: onde<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"105\" height=\"37\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-83.png\" alt=\"\" class=\"wp-image-145720\" style=\"width:71px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">l = lado do <span id=\"urn:enhancement-61405fa3-081e-4d1f-8196-4a59ca9d0121\" 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\">r = raio da <span id=\"urn:enhancement-ee61067b-ce5d-4091-bc08-43cd2e47bc3d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita, que tem o mesmo valor do ap&oacute;tema.<\/p><p class=\"wp-block-paragraph\">Para um <span id=\"urn:enhancement-677afc24-ff52-4bd0-813d-1d2cf7115e31\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero inscrito numa <span id=\"urn:enhancement-a109789f-d181-479e-bc6d-b2e20e3f93f8\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> (o <span id=\"urn:enhancement-4bb37a1b-6e82-42a8-9969-b024f4a64328\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> est&aacute; dentro do <span id=\"urn:enhancement-df83c10b-89f7-4931-8ccd-40e13ef4c03d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span>), temos que:<\/p><p class=\"wp-block-paragraph\">Lado (l): onde <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"105\" height=\"27\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-84.png\" alt=\"\" class=\"wp-image-145721\" style=\"width:78px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">o que nos leva a uma rela&ccedil;&atilde;o entre os raios<\/p><p class=\"wp-block-paragraph\">Onde R = 2r<\/p><h3 class=\"wp-block-heading\" id=\"h-quadrado-nbsp\">Quadrado&nbsp;<\/h3><p class=\"wp-block-paragraph\">O quadrado circunscrito tem seus lados tangentes &agrave; <span id=\"urn:enhancement-ddfdbe6f-b6bd-42f6-a358-308413cad5ec\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> e o raio da <span id=\"urn:enhancement-ad59a9d3-8e3f-4868-9100-ec6331ce2573\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita &eacute; r. Ao analisar, observa-se que o lado do quadrado &eacute; igual ao di&acirc;metro da <span id=\"urn:enhancement-73c40d1d-4ae9-4f2d-b0b4-45704ed0ca42\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita.&nbsp;<\/p><p class=\"wp-block-paragraph\">Sendo o di&acirc;metro da <span id=\"urn:enhancement-35aa7919-e130-47f9-8a5c-2221acd68a4b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>: 2r. Logo: l&#8324; = 2r<\/p><p class=\"wp-block-paragraph\">Tendo que o quadrado inscrito: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"103\" height=\"33\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-86.png\" alt=\"\" class=\"wp-image-145723\" style=\"width:87px;height:auto\"><\/figure><p class=\"wp-block-paragraph\"> e o quadrado circunscrito: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"78\" height=\"26\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-85.png\" alt=\"\" class=\"wp-image-145722\" style=\"width:66px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Calcula-se a rela&ccedil;&atilde;o entre r e R &eacute;: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"97\" height=\"31\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-87.png\" alt=\"\" class=\"wp-image-145724\" style=\"width:87px;height:auto\"><\/figure><h3 class=\"wp-block-heading\" id=\"h-hexagono-regular\">Hex&aacute;gono Regular<\/h3><p class=\"wp-block-paragraph\">O hex&aacute;gono regular possui uma propriedade &uacute;nica que &eacute; possuir o seu lado igual ao raio da <span id=\"urn:enhancement-8cb50866-20c5-4637-8d7a-a8b1a98426c8\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita (l&#8326; = R).<\/p><p class=\"wp-block-paragraph\">Contudo, para encontrar o valor do lado a partir do raio da <span id=\"urn:enhancement-fd0bbc51-d456-441c-8ce1-bce3b8047322\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> inscrita nele, utilizamos as seguintes rela&ccedil;&otilde;es:&nbsp;<\/p><p class=\"wp-block-paragraph\">A altura de um <span id=\"urn:enhancement-63c1d4ef-208b-4e61-9cee-02611751efc9\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> equil&aacute;tero de lado l &eacute; <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"129\" height=\"71\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-89.png\" alt=\"\" class=\"wp-image-145726\" style=\"width:84px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Neste caso, h = r e l = l&#8326;. Isolando l&#8326;: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"105\" height=\"73\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-90.png\" alt=\"\" class=\"wp-image-145727\" style=\"width:63px;height:auto\"><\/figure><p class=\"wp-block-paragraph\"> ou <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"131\" height=\"76\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-91.png\" alt=\"\" class=\"wp-image-145728\" style=\"width:107px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Vamos encontrar a rela&ccedil;&atilde;o para o mesmo hex&aacute;gono (com o mesmo lado l&#8326;). Do hex&aacute;gono inscrito: l&#8326; = R (propriedade fundamental) e do hex&aacute;gono circunscrito: <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"119\" height=\"64\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-92.png\" alt=\"\" class=\"wp-image-145729\" style=\"width:76px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Substituindo l&#8326; por R na segunda equa&ccedil;&atilde;o:<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"118\" height=\"72\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-93.png\" alt=\"\" class=\"wp-image-145730\" style=\"width:87px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Chega na rela&ccedil;&atilde;o <\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"100\" height=\"70\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-94.png\" alt=\"\" class=\"wp-image-145731\" style=\"width:70px;height:auto\"><\/figure><h2 class=\"wp-block-heading\" id=\"h-perimetro-e-area-de-poligonos-regulares-circunscritos-o-perimetro-de-um-poligono-regular-e-bem-tranquilo-de-calcular-basta-multiplicar-o-numero-de-lados-n-pelo-comprimento-de-um-lado-ln-ou-seja\"><span class=\"ez-toc-section\" id=\"Perimetro-e-Area-de-Poligonos-Regulares-Circunscritos-O-perimetro-de-um-poligono-regular-e-bem-tranquilo-de-calcular-basta-multiplicar-o-numero-de-lados-N-pelo-comprimento-de-um-lado-ln%E2%80%8B-ou-seja\"><\/span>Per&iacute;metro e &Aacute;rea de Pol&iacute;gonos Regulares Circunscritos:<br>O per&iacute;metro de um pol&iacute;gono regular &eacute; bem tranquilo de calcular, basta multiplicar o n&uacute;mero de lados N pelo comprimento de um lado ln&#8203;, ou seja,<span class=\"ez-toc-section-end\"><\/span><\/h2><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"141\" height=\"41\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-95.png\" alt=\"\" class=\"wp-image-145732\" style=\"width:100px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">A &aacute;rea pode ser obtida a partir da ideia de dividir o <span id=\"urn:enhancement-dfff2545-3e55-481d-81be-88a756862989\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> em <span id=\"urn:enhancement-e01def50-1c8c-4679-afc7-21fcbf6b6d5b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo\">tri&acirc;ngulos<\/span> is&oacute;sceles, todos com altura igual ao ap&oacute;tema r. Assim, a f&oacute;rmula geral &eacute;:<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"407\" height=\"56\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-96.png\" alt=\"\" class=\"wp-image-145733\" style=\"width:276px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Aten&ccedil;&atilde;o para alguns casos espec&iacute;ficos em que podemos substituir ln&#8203; em fun&ccedil;&atilde;o do ap&oacute;tema r. Por exemplo:<\/p><ul class=\"wp-block-list\">\n<li>Para n=3 (tri&acirc;ngulo equil&aacute;tero), <img decoding=\"async\" width=\"80\" height=\"28\" class=\"wp-image-145720\" style=\"width: 80px;\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-83.png\" alt=\"\"><br><\/li>\n\n\n\n<li>Para n=4 (quadrado), <img decoding=\"async\" width=\"60\" height=\"20\" class=\"wp-image-145722\" style=\"width: 60px;\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-85.png\" alt=\"\"><br><\/li>\n\n\n\n<li>Para n=6 (hex&aacute;gono regular), <img decoding=\"async\" width=\"80\" height=\"46\" class=\"wp-image-145728\" style=\"width: 80px;\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-91.png\" alt=\"\"><\/li>\n<\/ul><p class=\"wp-block-paragraph\">Assim, a &aacute;rea do <span id=\"urn:enhancement-a0f92a38-1464-452e-b3de-2f07f880bb31\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> regular pode ser expressa em fun&ccedil;&atilde;o de r, simplificando c&aacute;lculos em situa&ccedil;&otilde;es pr&aacute;ticas.<\/p><h2 class=\"wp-block-heading\" id=\"h-poligonos-inscritos-x-poligonos-circunscritos\"><span class=\"ez-toc-section\" id=\"Poligonos-Inscritos-X-Poligonos-Circunscritos\"><\/span>Pol&iacute;gonos Inscritos X Pol&iacute;gonos Circunscritos<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Ao tratar de <span id=\"urn:enhancement-9f84e872-f658-46a9-a0fc-10daa00f6b96\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligonos\">pol&iacute;gonos<\/span> regulares, podemos inscrev&ecirc;-los em uma <span id=\"urn:enhancement-ba90ab45-c6e2-4fa3-a3c5-a46ab59c8801\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> (todos os v&eacute;rtices sobre a <span id=\"urn:enhancement-af3e9111-b7f7-4cb0-b9f5-ef30c8efab21\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>) ou circunscrev&ecirc;-los a uma <span id=\"urn:enhancement-66ea8289-16ae-412d-876e-2c5e35fbbd6c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> (todos os lados tangentes &agrave; <span id=\"urn:enhancement-183fdf96-c5a3-4c67-abd4-2607e1d89158\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>).&nbsp;<\/p><p class=\"wp-block-paragraph\">Nos dois casos, aparecem: o lado do pol&iacute;gono, o raio da <span id=\"urn:enhancemen&lt;\/span&gt;t-f26ecc65-4b2a-4e41-a6e5-bafefadb3eda\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita (R) e o ap&oacute;tema (a&#8203; ou r), que &eacute; a <span id=\"urn:enhancement-accc7d1c-88fa-4c4e-9e2f-1487477389d6\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> do centro at&eacute; os lados.<\/p><p class=\"wp-block-paragraph\">Existe uma rela&ccedil;&atilde;o direta entre esses dois casos. Dado um n-l&aacute;tero regular com <span id=\"urn:enhancement-0484aba8-0987-4175-bf29-f27282251d99\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita de raio R, o ap&oacute;tema do <span id=\"urn:enhancement-cc3f1950-ad53-45c2-a509-5f241ee2e4fa\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> <strong>inscrito<\/strong> &eacute; o mesmo que o raio da <span id=\"urn:enhancement-d83113c9-7982-4d67-a8df-e1cb52b3dd5d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> <strong>inscrita<\/strong> no <span id=\"urn:enhancement-ed819ecf-4c73-4e3f-ad67-5197bae1dc40\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/poligono\">pol&iacute;gono<\/span> <strong>circunscrito<\/strong>.<\/p><h2 class=\"wp-block-heading\" id=\"h-questoes-sobre-poligonos-circunscritos\"><span class=\"ez-toc-section\" id=\"Questoes-sobre-poligonos-circunscritos\"><\/span>Quest&otilde;es sobre pol&iacute;gonos circunscritos<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-puc-pr-2016\">PUC -PR (2016)<\/h3><p class=\"wp-block-paragraph\">Um tri&acirc;ngulo possui uma t;\/span&gt;-4c1c-ab03-f7155c451ae2&Prime; class=&rdquo;textannotation disambiguated wl-thing&rdquo; itemid=&rdquo;https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia&rdquo;&gt;circunfer&ecirc;ncia inscrita e outra circunscrita. Um dos lados do <span id=\"urn:enhancement-d7993fa9-6ed6-4a33-9cbd-ff048044113b\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> passa pelo centro da <span id=\"urn:enhancement-159dd01b-d3b1-4fd4-8396-b956840d3acf\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> circunscrita e a soma das medidas dos outros lados &eacute; igual a s. Qual &eacute; a medida da soma dos comprimentos das duas <span id=\"urn:enhancement-00f527ee-82b6-4426-baf7-b258e440a599\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncias<\/span>?<\/p><p class=\"wp-block-paragraph\"><strong>A)<\/strong> &pi;s\/2<br><strong>B) <\/strong>&pi;s<br><strong>C)<\/strong> 2&pi;s\/3<br><strong>D)<\/strong> 2&pi;<br><strong>E)<\/strong> 3&pi;s\/2<\/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\">Precisamos encontrar os raios das duas <span id=\"urn:enhancement-fdacc325-6fef-488b-bc6d-c95b92e8e86e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncias<\/span> para calcular a soma de seus comprimentos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diametro c=2R<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pelo <strong>-ec242c58-5221-4eb2-b0f4-eb9bc398e32e&rdquo; class=&rdquo;textannotation disambiguated wl-thing&rdquo; itemid=&rdquo;https:\/\/data.wordlift.io\/wl110249\/entity\/teorema-de-pitagoras&rdquo;&gt;Teorema de Pit&aacute;goras<\/strong> no <s>pan id=&rdquo;urn:enhancement-6f1d1abe-c184-4f03-bcce-ef833e57b460&Prime; class=&rdquo;textannotation&rdquo;&gt;tri&acirc;ngulo ret&acirc;ngulo:<\/s><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"197\" height=\"234\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-97.png\" alt=\"\" class=\"wp-image-145735\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"839\" height=\"394\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-99.png\" alt=\"\" class=\"wp-image-145737\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-99.png 839w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-99-768x361.png 768w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-99-800x376.png 800w\" sizes=\"(max-width: 839px) 100vw, 839px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"847\" height=\"352\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-100.png\" alt=\"\" class=\"wp-image-145738\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-100.png 847w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-100-768x319.png 768w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-100-800x332.png 800w\" sizes=\"(max-width: 847px) 100vw, 847px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"746\" height=\"457\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-98.png\" alt=\"\" class=\"wp-image-145736\" style=\"width:539px;height:auto\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sc=&pi;s<br>Alternativa correta:&nbsp;<strong>B<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<\/details><p class=\"wp-block-paragraph\">Sc=&pi;s<\/p><p class=\"wp-block-paragraph\">Alternativa correta: <strong>B<\/strong><\/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\">Conquiste sua vaga na universidade com o Estrat&eacute;gia Vestibulares!<\/p><p class=\"wp-block-paragraph\">Aqui voc&ecirc; tem acesso a materiais completos, atualizados e focados nos conte&uacute;dos que mais caem nas provas.&nbsp;<\/p><p class=\"wp-block-paragraph\">Com nossos planos, voc&ecirc; pode personalizar seus estudos, direcionando tempo e energia para os assuntos que realmente v&atilde;o fazer diferen&ccedil;a no seu resultado.<\/p><p class=\"wp-block-paragraph\">Clique no banner e saiba mais!<\/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 pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas.\n","protected":false},"author":61,"featured_media":145742,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-145709","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 Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es<\/title>\n<meta name=\"description\" content=\"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es\" \/>\n<meta property=\"og:description\" content=\"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/\" \/>\n<meta property=\"og:site_name\" content=\"Estrat\u00e9gia Vestibulares\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/facebook.com\/estrategiavestibulares\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-30T15:34:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-08T18:53:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"1024\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Caiky Pinheiro\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@Estrategiavest\" \/>\n<meta name=\"twitter:site\" content=\"@Estrategiavest\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Caiky Pinheiro\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/\"},\"author\":{\"name\":\"Caiky Pinheiro\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#\\\/schema\\\/person\\\/c7f508351071581779a499fb483e23ed\"},\"headline\":\"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es\",\"datePublished\":\"2025-09-30T15:34:19+00:00\",\"dateModified\":\"2025-10-08T18:53:19+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/\"},\"wordCount\":1531,\"publisher\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/pexels-yankrukov-8617701.jpg\",\"articleSection\":[\"Matem\u00e1tica\"],\"inLanguage\":\"pt-BR\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/\",\"name\":\"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/pexels-yankrukov-8617701.jpg\",\"datePublished\":\"2025-09-30T15:34:19+00:00\",\"dateModified\":\"2025-10-08T18:53:19+00:00\",\"description\":\"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#primaryimage\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/pexels-yankrukov-8617701.jpg\",\"contentUrl\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2025\\\/09\\\/pexels-yankrukov-8617701.jpg\",\"width\":1280,\"height\":1024,\"caption\":\"poligonos-circunscritos-na-circunferencia-vestibular\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Mat\u00e9rias\",\"item\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matem\u00e1tica\",\"item\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/materias\\\/matematica\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#website\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/\",\"name\":\"Estrat\u00e9gia Vestibulares\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#organization\",\"name\":\"Estrat\u00e9gia Vestibulares\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2021\\\/06\\\/Logo-Vestibulares@4x.png\",\"contentUrl\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/wp-content\\\/uploads\\\/2021\\\/06\\\/Logo-Vestibulares@4x.png\",\"width\":250,\"height\":66,\"caption\":\"Estrat\u00e9gia Vestibulares\"},\"image\":{\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/facebook.com\\\/estrategiavestibulares\",\"https:\\\/\\\/x.com\\\/Estrategiavest\",\"https:\\\/\\\/www.instagram.com\\\/estrategiavestibulares\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UCGWdZy8ULI-7_5GrABa4vNA\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/#\\\/schema\\\/person\\\/c7f508351071581779a499fb483e23ed\",\"name\":\"Caiky Pinheiro\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g\",\"caption\":\"Caiky Pinheiro\"},\"description\":\"Redator do Portal Estrat\u00e9gia Vestibulares e estudante de Matem\u00e1tica Aplicada na Unicamp.\",\"url\":\"https:\\\/\\\/vestibulares.estrategia.com\\\/portal\\\/author\\\/caiky-pinheiro\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es","description":"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/","og_locale":"pt_BR","og_type":"article","og_title":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es","og_description":"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas","og_url":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/","og_site_name":"Estrat\u00e9gia Vestibulares","article_publisher":"https:\/\/facebook.com\/estrategiavestibulares","article_published_time":"2025-09-30T15:34:19+00:00","article_modified_time":"2025-10-08T18:53:19+00:00","og_image":[{"width":1280,"height":1024,"url":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg","type":"image\/jpeg"}],"author":"Caiky Pinheiro","twitter_card":"summary_large_image","twitter_creator":"@Estrategiavest","twitter_site":"@Estrategiavest","twitter_misc":{"Escrito por":"Caiky Pinheiro","Est. tempo de leitura":"8 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#article","isPartOf":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/"},"author":{"name":"Caiky Pinheiro","@id":"https:\/\/vestibulares.estrategia.com\/portal\/#\/schema\/person\/c7f508351071581779a499fb483e23ed"},"headline":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es","datePublished":"2025-09-30T15:34:19+00:00","dateModified":"2025-10-08T18:53:19+00:00","mainEntityOfPage":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/"},"wordCount":1531,"publisher":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/#organization"},"image":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#primaryimage"},"thumbnailUrl":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg","articleSection":["Matem\u00e1tica"],"inLanguage":"pt-BR"},{"@type":"WebPage","@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/","url":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/","name":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es","isPartOf":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/#website"},"primaryImageOfPage":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#primaryimage"},"image":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#primaryimage"},"thumbnailUrl":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg","datePublished":"2025-09-30T15:34:19+00:00","dateModified":"2025-10-08T18:53:19+00:00","description":"Entenda mais sobre pol\u00edgonos circunscritos na circunfer\u00eancia e como usar as rela\u00e7\u00f5es geom\u00e9tricas para resolver situa\u00e7\u00f5es problemas","breadcrumb":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/"]}]},{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#primaryimage","url":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg","contentUrl":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/pexels-yankrukov-8617701.jpg","width":1280,"height":1024,"caption":"poligonos-circunscritos-na-circunferencia-vestibular"},{"@type":"BreadcrumbList","@id":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/poligonos-circunscritos-na-circunferencia-formulas-e-aplicacoes\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/vestibulares.estrategia.com\/portal\/"},{"@type":"ListItem","position":2,"name":"Mat\u00e9rias","item":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/"},{"@type":"ListItem","position":3,"name":"Matem\u00e1tica","item":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/"},{"@type":"ListItem","position":4,"name":"Pol\u00edgonos Circunscritos na Circunfer\u00eancia: F\u00f3rmulas e Aplica\u00e7\u00f5es"}]},{"@type":"WebSite","@id":"https:\/\/vestibulares.estrategia.com\/portal\/#website","url":"https:\/\/vestibulares.estrategia.com\/portal\/","name":"Estrat\u00e9gia Vestibulares","description":"","publisher":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vestibulares.estrategia.com\/portal\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/vestibulares.estrategia.com\/portal\/#organization","name":"Estrat\u00e9gia Vestibulares","url":"https:\/\/vestibulares.estrategia.com\/portal\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/vestibulares.estrategia.com\/portal\/#\/schema\/logo\/image\/","url":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2021\/06\/Logo-Vestibulares@4x.png","contentUrl":"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2021\/06\/Logo-Vestibulares@4x.png","width":250,"height":66,"caption":"Estrat\u00e9gia Vestibulares"},"image":{"@id":"https:\/\/vestibulares.estrategia.com\/portal\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/facebook.com\/estrategiavestibulares","https:\/\/x.com\/Estrategiavest","https:\/\/www.instagram.com\/estrategiavestibulares","https:\/\/www.youtube.com\/channel\/UCGWdZy8ULI-7_5GrABa4vNA"]},{"@type":"Person","@id":"https:\/\/vestibulares.estrategia.com\/portal\/#\/schema\/person\/c7f508351071581779a499fb483e23ed","name":"Caiky Pinheiro","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/secure.gravatar.com\/avatar\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/581b7703750b5199213f75080312fb21d4d9c345c3b6da1512bfca922df89180?s=96&d=mm&r=g","caption":"Caiky Pinheiro"},"description":"Redator do Portal Estrat\u00e9gia Vestibulares e estudante de Matem\u00e1tica Aplicada na Unicamp.","url":"https:\/\/vestibulares.estrategia.com\/portal\/author\/caiky-pinheiro\/"}]}},"_links":{"self":[{"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/posts\/145709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/users\/61"}],"replies":[{"embeddable":true,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/comments?post=145709"}],"version-history":[{"count":9,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/posts\/145709\/revisions"}],"predecessor-version":[{"id":145976,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/posts\/145709\/revisions\/145976"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/media\/145742"}],"wp:attachment":[{"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/media?parent=145709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/categories?post=145709"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vestibulares.estrategia.com\/portal\/wp-json\/wp\/v2\/tags?post=145709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}