{"id":144487,"date":"2025-08-29T15:13:09","date_gmt":"2025-08-29T18:13:09","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=144487"},"modified":"2025-09-08T16:08:00","modified_gmt":"2025-09-08T19:08:00","slug":"eixo-radical-definicao-aplicacoes-questoes-e-mais","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/","title":{"rendered":"Eixo radical: defini\u00e7\u00e3o, aplica\u00e7\u00f5es, quest\u00f5es e mais"},"content":{"rendered":"<p class=\"wp-block-paragraph\">As circunfer&ecirc;ncias s&atilde;o figuras muito presentes no estudo da <span id=\"urn:enhancement-626c314a-b73b-402c-b2ae-00d1b416adaa\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria-analitica\">Geometria Anal&iacute;tica<\/span>. Entre as diversas propriedades relacionadas &agrave;s circunfer&ecirc;ncias, temos o <span id=\"urn:enhancement-0aaa0ad0-265e-48e0-9764-b66a9acc75ad\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical, uma ferramenta &uacute;til e pr&aacute;tica para resolu&ccedil;&atilde;o de problemas envolvendo duas ou mais circunfer&ecirc;ncias.<p class=\"wp-block-paragraph\">Entender esse assunto &eacute; importante para quem quer ir bem no <span id=\"urn:enhancement-4f72c7d3-3ca5-42dd-bc64-38648004713e\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/exame-nacional-do-ensino-medio-2\">Enem<\/span> e vestibulares, pois ele aparece em algumas quest&otilde;es de <span id=\"urn:enhancement-1b61857d-2f25-48b9-b4c3-8bbe21b9b289\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/matematica\">Matem&aacute;tica<\/span>. Neste texto, iremos explorar o tema de maneira did&aacute;tica, para que voc&ecirc; compreenda n&atilde;o apenas as f&oacute;rmulas, mas tamb&eacute;m o racioc&iacute;nio e a l&oacute;gica por tr&aacute;s delas. Vamos l&aacute;?<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Relembrando-potencia-de-ponto\" >Relembrando pot&ecirc;ncia de ponto<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Definicao-de-eixo-radical\" >Defini&ccedil;&atilde;o de eixo radical<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Propriedades-do-eixo-radical\" >Propriedades do eixo radical<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Encontrando-a-equacao-do-eixo-radical\" >Encontrando a equa&ccedil;&atilde;o do eixo radical<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Aplicacoes-do-eixo-radical\" >Aplica&ccedil;&otilde;es do eixo radical<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Erros-comuns\" >Erros comuns<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Centro-radical\" >Centro radical<\/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\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Questao-sobre-eixo-radical\" >Quest&atilde;o sobre eixo radical<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/eixo-radical-definicao-aplicacoes-questoes-e-mais\/#Estude-com-o-Estrategia-Vestibulares\" >Estude com o Estrat&eacute;gia Vestibulares!<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-relembrando-potencia-de-ponto\"><span class=\"ez-toc-section\" id=\"Relembrando-potencia-de-ponto\"><\/span>Relembrando pot&ecirc;ncia de ponto<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Antes de falar sobre o <span id=\"urn:enhancement-8c6f2a51-ed27-49a8-ae09-a80619099df9\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical, precisamos relembrar o conceito de <a href=\"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/potencia-de-ponto-definicao-formulas-questoes-e-mais\/\" target=\"_blank\">Pot&ecirc;ncia de Ponto<\/a>. Nesse contexto, para uma <span id=\"urn:enhancement-96683865-ed12-466c-a256-4b5a8bd34852\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> qualquer, temos diferentes rela&ccedil;&otilde;es m&eacute;tricas entre segmentos internos, tangentes e secantes que se cruzam em um ponto interno ou externo &agrave; <span id=\"urn:enhancement-134b164a-a26b-495a-b4d0-bacc8ab49010\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>.<\/p><p class=\"wp-block-paragraph\">H&aacute; tr&ecirc;s casos principais em que utilizamos a pot&ecirc;ncia de ponto:<\/p><ul class=\"wp-block-list\">\n<li><strong>Ponto interno <\/strong>(duas cordas se cruzando no interior da circunfer&ecirc;ncia): O produto dos segmentos de uma corda &eacute; igual ao produto dos segmentos da outra.<\/li>\n<\/ul><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"212\" height=\"223\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/Captura-de-Tela-1.png\" alt=\"\" class=\"wp-image-144468\"><\/figure>\n<\/div><p class=\"has-text-align-center wp-block-paragraph\"><strong>a . b = c . d<\/strong><\/p><ul class=\"wp-block-list\">\n<li><strong>Ponto externo com duas secantes: <\/strong>O comprimento total de cada secante multiplicado pela sua parte externa tem o mesmo valor para as duas secantes.<\/li>\n<\/ul><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"498\" height=\"403\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/Captura-de-Tela-3.png\" alt=\"\" class=\"wp-image-144470\" style=\"width:256px;height:auto\"><\/figure>\n<\/div><p class=\"has-text-align-center wp-block-paragraph\"><strong>a . (a + b) = c . (c + d)<\/strong><\/p><ul class=\"wp-block-list\">\n<li><strong>Ponto interno com uma secante e uma tangente: <\/strong>O produto da secante pelo seu trecho externo &eacute; igual ao quadrado da tangente.<\/li>\n<\/ul><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"577\" height=\"426\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/Captura-de-Tela-4.png\" alt=\"\" class=\"wp-image-144471\" style=\"width:273px;height:auto\"><\/figure>\n<\/div><p class=\"has-text-align-center wp-block-paragraph\"><strong>a . (a + b) = c<\/strong><strong><sup>2<\/sup><\/strong><\/p><h2 class=\"wp-block-heading\" id=\"h-definicao-de-eixo-radical\"><span class=\"ez-toc-section\" id=\"Definicao-de-eixo-radical\"><\/span>Defini&ccedil;&atilde;o de eixo radical<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">O <span id=\"urn:enhancement-abf7b19e-6579-47b1-b970-b640a05b6f83\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical de duas circunfer&ecirc;ncias n&atilde;o conc&ecirc;ntricas &eacute; o conjunto de pontos que t&ecirc;m a mesma pot&ecirc;ncia em rela&ccedil;&atilde;o a ambas. Essa <span id=\"urn:enhancement-4210bca0-33b2-481a-be28-9d8e31eb5435\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/axiomas\">afirma&ccedil;&atilde;o<\/span>, em termos <span id=\"urn:enhancement-e2411797-23fd-42c8-870c-f9352a750d5a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;tricos<\/span>, significa que, para qualquer ponto P do <span id=\"urn:enhancement-ec997e50-cdb4-41a6-a8fe-50403796952f\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical, os segmentos de reta tra&ccedil;ados de P para cada uma das circunfer&ecirc;ncias t&ecirc;m o mesmo comprimento. Em outras palavras, P &ldquo;v&ecirc;&rdquo; as duas circunfer&ecirc;ncias do mesmo jeito.<\/p><p class=\"wp-block-paragraph\">Para duas circunfer&ecirc;ncias que se intersectam em dois pontos distintos, o <span id=\"urn:enhancement-7169c9f2-a901-49cd-b41e-8570e3ee77a0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical ser&aacute; a reta que une esses dois pontos. J&aacute; para duas circunfer&ecirc;ncias tangentes, o <span id=\"urn:enhancement-b1ac93e4-0aa4-4ded-b408-971d327dd680\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical &eacute; a tangente comum &agrave;s duas circunfer&ecirc;ncias que passa pelo ponto de intersec&ccedil;&atilde;o.<\/p><p class=\"wp-block-paragraph\">&Eacute; importante se atentar ao fato de que, se as circunfer&ecirc;ncias forem conc&ecirc;ntricas (mesmo centro), o <span id=\"urn:enhancement-794ff6d3-e1cd-4ada-ba61-6e50c293a5d9\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical n&atilde;o existe, pois todos os pontos ter&atilde;o pot&ecirc;ncias diferentes, j&aacute; que os raios s&atilde;o distintos mas a <span id=\"urn:enhancement-7b044798-e932-43a0-8974-dd110c3505cb\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> ao centro &eacute; a mesma.<\/p><h2 class=\"wp-block-heading\" id=\"h-propriedades-do-eixo-radical\"><span class=\"ez-toc-section\" id=\"Propriedades-do-eixo-radical\"><\/span>Propriedades do eixo radical<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">O <span id=\"urn:enhancement-107b9171-c7ea-4395-a951-04cf60674a1a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical n&atilde;o &eacute; apenas um conceito abstrato; ele possui propriedades bem definidas que facilitam sua visualiza&ccedil;&atilde;o e aplica&ccedil;&atilde;o em problemas pr&aacute;ticos:<\/p><ul class=\"wp-block-list\">\n<li><strong>&Eacute; sempre uma reta<\/strong>: ao subtrair as equa&ccedil;&otilde;es das duas circunfer&ecirc;ncias, os termos quadr&aacute;ticos desaparecem, restando uma equa&ccedil;&atilde;o linear que representa uma reta.<\/li>\n\n\n\n<li><strong>&Eacute; perpendicular &agrave; reta que liga os centros das circunfer&ecirc;ncias<\/strong>: essa rela&ccedil;&atilde;o de perpendicularidade &eacute; essencial para entender a geometria do problema e para tra&ccedil;ar esbo&ccedil;os que ajudam na resolu&ccedil;&atilde;o.<\/li>\n\n\n\n<li><strong>Comportamento em diferentes casos<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Circunfer&ecirc;ncias secantes<\/strong>: o eixo radical passa pelos dois pontos de interse&ccedil;&atilde;o.<\/li>\n\n\n\n<li><strong>Circunfer&ecirc;ncias tangentes<\/strong>: o eixo radical &eacute; a reta tangente comum no ponto de tang&ecirc;ncia.<\/li>\n\n\n\n<li><strong>Circunfer&ecirc;ncias externas ou internas sem interse&ccedil;&atilde;o<\/strong>: o eixo radical existe, mas n&atilde;o toca nenhuma das circunfer&ecirc;ncias; ele fica &ldquo;entre elas&rdquo; ou fora, dependendo das posi&ccedil;&otilde;es e raios.<\/li>\n<\/ul>\n<\/li>\n<\/ul><h2 class=\"wp-block-heading\" id=\"h-encontrando-a-equacao-do-eixo-radical\"><span class=\"ez-toc-section\" id=\"Encontrando-a-equacao-do-eixo-radical\"><\/span>Encontrando a equa&ccedil;&atilde;o do eixo radical<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Na pr&aacute;tica, os problemas de vestibular muitas vezes pedem a equa&ccedil;&atilde;o do <span id=\"urn:enhancement-4b0e6c0e-f697-417b-b107-ec8b3e247dba\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical a partir das equa&ccedil;&otilde;es das circunfer&ecirc;ncias.<\/p><p class=\"wp-block-paragraph\">Suponha que temos as equa&ccedil;&otilde;es gerais de duas circunfer&ecirc;ncias:<\/p><p class=\"has-text-align-center wp-block-paragraph\">x<sup>2<\/sup> + y<sup>2<\/sup> + A<sub>1<\/sub>x + B<sub>1<\/sub>y + C<sub>1<\/sub> = 0<\/p><p class=\"has-text-align-center wp-block-paragraph\">x<sup>2<\/sup> + y<sup>2<\/sup> + A<sub>2<\/sub>x + B<sub>2<\/sub>y + C<sub>2<\/sub> = 0<\/p><p class=\"wp-block-paragraph\">Se subtrairmos as equa&ccedil;&otilde;es, os termos x<sup>2<\/sup> e y<sup>2<\/sup> se anulam, e obtemos:<\/p><p class=\"has-text-align-center wp-block-paragraph\"><strong>(A<\/strong><strong><sub>1<\/sub><\/strong><strong> &ndash; A<\/strong><strong><sub>2<\/sub><\/strong><strong>)x + (B<\/strong><strong><sub>1<\/sub><\/strong><strong> &ndash; B<\/strong><strong><sub>2<\/sub><\/strong><strong>)y + (C<\/strong><strong><sub>1<\/sub><\/strong><strong> &ndash; C<\/strong><strong><sub>2<\/sub><\/strong><strong>) = 0<\/strong><\/p><p class=\"wp-block-paragraph\">Essa &eacute; uma equa&ccedil;&atilde;o linear, a qual representa a reta do <span id=\"urn:enhancement-a5e5640f-49a9-4004-bac2-ce199d601eb1\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical.<\/p><h2 class=\"wp-block-heading\" id=\"h-aplicacoes-do-eixo-radical\"><span class=\"ez-toc-section\" id=\"Aplicacoes-do-eixo-radical\"><\/span>Aplica&ccedil;&otilde;es do eixo radical<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">O <span id=\"urn:enhancement-fb1697c9-b5dd-4ad5-8cc8-4f3573eed2e5\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical &eacute; mais do que apenas uma reta no <span id=\"urn:enhancement-f5a6f5eb-e12c-4a5c-a555-550fc522610a\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano\">plano<\/span>. Ele re&uacute;ne conceitos de <span id=\"urn:enhancement-53119759-b043-4486-a608-fd96f0ca7b70\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geometria<\/span> e <span id=\"urn:enhancement-4063b451-327b-4b65-a276-6234882c00cb\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/algebra\">&aacute;lgebra<\/span> em uma ferramenta vers&aacute;til para resolver problemas que envolvem duas ou mais circunfer&ecirc;ncias.&nbsp;<\/p><p class=\"wp-block-paragraph\">Ao entender o conceito de pot&ecirc;ncia de um ponto, a defini&ccedil;&atilde;o e as propriedades do <span id=\"urn:enhancement-a72b76bd-54e6-4772-8e52-aa18de5649dc\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical, al&eacute;m de saber como encontrar sua equa&ccedil;&atilde;o, voc&ecirc; ter&aacute; em m&atilde;os um recurso poderoso para enfrentar problemas de <span id=\"urn:enhancement-76e32540-2254-4cfa-8d12-898fd64f2008\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria-analitica\">geometria anal&iacute;tica<\/span>, pois o <span id=\"urn:enhancement-9bd03cb0-d793-48f2-a709-bea16d60f30b\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical n&atilde;o &eacute; apenas um conceito te&oacute;rico, ele tem diversas aplica&ccedil;&otilde;es importantes, como:<\/p><ul class=\"wp-block-list\">\n<li>Determinar a reta que cont&eacute;m a corda comum entre duas circunfer&ecirc;ncias secantes;<\/li>\n\n\n\n<li>Encontrar a reta tangente comum quando as circunfer&ecirc;ncias s&atilde;o tangentes; e<\/li>\n\n\n\n<li>Localizar pontos que t&ecirc;m tangentes de mesmo comprimento para duas circunfer&ecirc;ncias.<\/li>\n<\/ul><h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Erros-comuns\"><\/span>Erros comuns<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Ao estudar o <span id=\"urn:enhancement-9cfd0765-d1fa-4387-9a3f-3bfbab59efa6\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical, alguns erros aparecem com frequ&ecirc;ncia:<\/p><ul class=\"wp-block-list\">\n<li><strong>Tentar calcular o eixo radical para circunfer&ecirc;ncias conc&ecirc;ntricas<\/strong>: n&atilde;o existe, j&aacute; que todos os pontos t&ecirc;m pot&ecirc;ncias diferentes.<\/li>\n\n\n\n<li><strong>Erros alg&eacute;bricos ao subtrair as equa&ccedil;&otilde;es<\/strong>: &eacute; comum se perder nos sinais.<\/li>\n<\/ul><p class=\"wp-block-paragraph\"><strong>Confundir o <span id=\"urn:enhancement-97656c89-3b6b-4f8e-954a-d20c7fa3c267\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical com a linha dos centros<\/strong>: lembre-se, eles s&atilde;o perpendiculares!<\/p><h2 class=\"wp-block-heading\" id=\"h-centro-radical\"><span class=\"ez-toc-section\" id=\"Centro-radical\"><\/span>Centro radical<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Quando temos tr&ecirc;s circunfer&ecirc;ncias, os <span id=\"urn:enhancement-1cea619a-a74e-407d-8946-e7664cab12c4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/coordenadas-cartesianas\">eixos<\/span> radicais tomados dois a dois se cruzam em um ponto denominado centro radical. Esse ponto tem a mesma pot&ecirc;ncia em rela&ccedil;&atilde;o &agrave;s tr&ecirc;s circunfer&ecirc;ncias, o que pode ser &uacute;til em problemas de de concorr&ecirc;ncia de retas e outras propriedades <span id=\"urn:enhancement-2b5fb28b-a5ef-49e9-9f42-2cc1e9a383fa\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;tricas<\/span>.<\/p><h2 class=\"wp-block-heading\" id=\"h-questao-sobre-eixo-radical\"><span class=\"ez-toc-section\" id=\"Questao-sobre-eixo-radical\"><\/span>Quest&atilde;o sobre eixo radical<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-questao-inedita-estrategia-militares-2021\">Quest&atilde;o in&eacute;dita &ndash; Estrat&eacute;gia Militares (2021)<\/h3><p class=\"wp-block-paragraph\">Considere os c&iacute;rculos da figura de raios 10 e 4 e seu <span id=\"urn:enhancement-1dd9fff4-b2bd-4f08-ba00-da319f52d9d4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical. Se&nbsp; &eacute; tangente em J ao <span id=\"urn:enhancement-82dc368f-7de3-4ca1-9f3a-cdec34ccee27\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span> menor, calcule a &aacute;rea do <span id=\"urn:enhancement-7cfc4b0f-37da-4b5d-972d-2216bcb1e39d\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/triangulo-2\">tri&acirc;ngulo<\/span> ATH.<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"400\" height=\"377\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-20.png\" alt=\"\" class=\"wp-image-144503\" style=\"width:291px;height:auto\"><\/figure><details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Resolu&ccedil;&atilde;o<\/summary>\n<p class=\"wp-block-paragraph\">GABARITO: (11881)\/(150)&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se J &eacute; o ponto de tang&ecirc;ncia e o raio do <span id=\"urn:enhancement-9cf911ce-15df-4148-bb72-eec17db1b93d\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circulo\">c&iacute;rculo<\/span> menor &eacute; 4, ent&atilde;o, o tri&acirc;ngulo ret&acirc;ngulo ABJ &eacute; o tri&acirc;ngulo ret&acirc;ngulo 3:4:5. Vamos inserir as vari&aacute;veis na figura:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"393\" height=\"400\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-22.png\" alt=\"\" class=\"wp-image-144508\" style=\"width:234px;height:auto\"><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"324\" height=\"53\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-21.png\" alt=\"\" class=\"wp-image-144506\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos encontrar o valor de x, usando a defini&ccedil;&atilde;o de <span id=\"urn:enhancement-a649a79a-8c6d-47e9-9d4c-15d5ecce7554\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/eixo-de-rotacao\">eixo<\/span> radical:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"324\" height=\"53\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-21.png\" alt=\"\" class=\"wp-image-144505\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Analisando o tri&acirc;ngulo ret&acirc;ngulo ABJ, temos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">tg&alpha;=(4)\/(3)&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos encontrar a altura TH:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"324\" height=\"53\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-21.png\" alt=\"\" class=\"wp-image-144504\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A &aacute;rea do &Delta;ATH &eacute; dada por:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"324\" height=\"53\" fetchpriority=\"low\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/08\/image-21.png\" alt=\"\" class=\"wp-image-144507\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<\/details><h2 class=\"wp-block-heading\" id=\"h-estude-com-o-estrategia-vestibulares\"><span class=\"ez-toc-section\" id=\"Estude-com-o-Estrategia-Vestibulares\"><\/span>Estude com o Estrat&eacute;gia Vestibulares!<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">Prepare-se para o <span id=\"urn:enhancement-3fd39731-4af4-44ff-a779-f966090a983f\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/exame-nacional-do-ensino-medio-2\">Enem<\/span> e vestibulares com os cursos da Coruja! Na plataforma do EV, voc&ecirc; ter&aacute; acesso aos melhores materiais para a sua prepara&ccedil;&atilde;o, com um banco de quest&otilde;es exclusivo, conte&uacute;dos em v&iacute;deo e pdf, al&eacute;m de f&oacute;rum de d&uacute;vidas para falar direto com os professores. Clique no banner abaixo e seja nosso aluno!<\/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":"Aprenda a defini\u00e7\u00e3o, aplica\u00e7\u00f5es e f\u00f3rmulas envolvendo eixo radical, para conseguir resolver as quest\u00f5es de geometria do vestibular\n","protected":false},"author":58,"featured_media":144519,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-144487","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>Eixo radical: defini\u00e7\u00e3o, aplica\u00e7\u00f5es, quest\u00f5es e mais<\/title>\n<meta name=\"description\" content=\"Aprenda a defini\u00e7\u00e3o, aplica\u00e7\u00f5es e f\u00f3rmulas envolvendo eixo radical, para conseguir resolver as quest\u00f5es de geometria do vestibular.\" \/>\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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