{"id":145693,"date":"2025-09-30T11:50:45","date_gmt":"2025-09-30T14:50:45","guid":{"rendered":"https:\/\/vestibulares.estrategia.com\/portal\/?p=145693"},"modified":"2025-10-08T10:50:12","modified_gmt":"2025-10-08T13:50:12","slug":"posicoes-relativas-entre-reta-e-circunferencia","status":"publish","type":"post","link":"https:\/\/vestibulares.estrategia.com\/portal\/materias\/matematica\/posicoes-relativas-entre-reta-e-circunferencia\/","title":{"rendered":"Posi\u00e7\u00f5es Relativas entre Reta e Circunfer\u00eancia"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Um dos t&oacute;picos mais cobrados que relaciona <span id=\"urn:enhancement-fe3e76a8-9672-45b7-b2f3-599789e8c9ed\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">Geometria<\/span> Pura e Anal&iacute;tica, que aparece com frequ&ecirc;ncia no <span id=\"urn:enhancement-56892e43-00f6-464b-8413-5033623946e0\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/exame-nacional-do-ensino-medio-2\">Enem<\/span> e outros vestibulares, &eacute; o estudo das <strong>posi&ccedil;&otilde;es relativas entre reta e <span id=\"urn:enhancement-d75d370b-c46e-4deb-91b0-9499fa745aba\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span><\/strong>.&nbsp;<p class=\"wp-block-paragraph\">Esse conte&uacute;do aborda c&aacute;lculos de geometria anal&iacute;tica com a combina&ccedil;&atilde;o da equa&ccedil;&atilde;o da reto juntamente com equa&ccedil;&atilde;o que descreve a <span id=\"urn:enhancement-1da98471-5465-4f03-8362-9075384ed9da\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Veja mais sobre esse assunto no artigo do EV a seguir:<\/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\/posicoes-relativas-entre-reta-e-circunferencia\/#Elementos-Principais\" >Elementos Principais<\/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\/posicoes-relativas-entre-reta-e-circunferencia\/#Retas-e-numero-de-interseccoes\" >Retas e n&uacute;mero de intersec&ccedil;&otilde;es<\/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\/posicoes-relativas-entre-reta-e-circunferencia\/#Visao-geral\" >Vis&atilde;o geral<\/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\/posicoes-relativas-entre-reta-e-circunferencia\/#Questoes-sobre-posicao-relativa-entre-circunferencia-e-reta\" >Quest&otilde;es sobre posi&ccedil;&atilde;o relativa entre circunfer&ecirc;ncia e reta<\/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\/posicoes-relativas-entre-reta-e-circunferencia\/#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-elementos-principais\"><span class=\"ez-toc-section\" id=\"Elementos-Principais\"><\/span>Elementos Principais<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">A posi&ccedil;&atilde;o que uma reta ocupa em rela&ccedil;&atilde;o a uma <span id=\"urn:enhancement-53914f31-5709-4ff4-8567-3ead75beb4e0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> tem diferentes classifica&ccedil;&otilde;es, cada uma com suas propriedades e caracter&iacute;sticas. Para compreend&ecirc;-las veja os principais elementos que comp&otilde;em essas figuras geom&eacute;tricas.<\/p><p class=\"wp-block-paragraph\">Primeiramente a <strong><span id=\"urn:enhancement-a7f3c5ae-e97e-4854-a4ac-0ecf9d069f19\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span><\/strong>, ela &eacute; um dos conceitos fundamentais da <span id=\"urn:enhancement-bddca26e-be74-4236-b8ee-b36797921478\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria-euclidiana\">Geometria Plana<\/span>. Para entend&ecirc;-la, imagine um ponto fixo em um <span id=\"urn:enhancement-a1469329-b4a1-4402-991d-d47437e8d85a\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano\">plano<\/span>, chamado centro (C). A partir desse ponto, considere todos os pontos que est&atilde;o exatamente a uma mesma <span id=\"urn:enhancement-daef9319-64b7-44ae-8886-dad0d50c2893\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> dele.&nbsp;<\/p><p class=\"wp-block-paragraph\">O conjunto formado por esses pontos gera uma linha curva fechada chamada de <span id=\"urn:enhancement-c963fdbd-c664-485b-918d-bee95a9822d3\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. A <span id=\"urn:enhancement-62c194cf-3f8e-4560-a73a-02a310e3d1c3\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> constante entre o centro (ponto rosa) e qualquer ponto da <span id=\"urn:enhancement-5850a21d-f4ab-4a38-97f4-0286c77edd61\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> recebe o nome de raio (r).<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"395\" height=\"375\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-73.png\" alt=\"\" class=\"wp-image-145701\" style=\"width:169px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Outro elemento associado &agrave; <span id=\"urn:enhancement-ea60659f-edc5-4d1e-900c-17d3a295040e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> &eacute; o <strong>di&acirc;metro<\/strong> (d). Ele corresponde ao segmento de reta que atravessa o centro e conecta <span id=\"urn:enhancement-4ac2de25-4666-4cb5-aaad-932c50a35e26\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/dois-pontos\">dois pontos<\/span> opostos da <span id=\"urn:enhancement-3e21e10e-705f-4e31-9fff-042e28bb6fb8\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Por defini&ccedil;&atilde;o, o comprimento do di&acirc;metro &eacute; o dobro do raio (d=2r).<\/p><p class=\"wp-block-paragraph\">Ainda sobre a <span id=\"urn:enhancement-08a70d72-7f13-4c03-a675-b9f640937495\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> temos a <strong>corda<\/strong>, segmento de reta que une <span id=\"urn:enhancement-33aaa60d-6245-4413-8a54-bd9a957e0abd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/dois-pontos\">dois pontos<\/span> distintos da <span id=\"urn:enhancement-a4ed1224-59d6-4140-8861-7d2f18fb5902\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>, podendo ter diferentes comprimentos &mdash; sendo o di&acirc;metro a maior corda poss&iacute;vel.&nbsp;<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"583\" height=\"416\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-74.png\" alt=\"\" class=\"wp-image-145702\" style=\"width:307px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">A <strong>reta<\/strong> pode ser compreendida como uma linha infinita, sem curvas, que se prolonga indefinidamente em ambas as dire&ccedil;&otilde;es. No <span id=\"urn:enhancement-eba89154-1433-43dd-b927-f37001bc7ad0\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano-cartesiano\">plano cartesiano<\/span>, ela &eacute; descrita por uma equa&ccedil;&atilde;o, geralmente em sua <span id=\"urn:enhancement-353c8eac-a6d4-4d5a-a965-10e48f1f7f74\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> geral: ax+by+c=0, em que a, b e c s&atilde;o n&uacute;meros reais. Essa representa&ccedil;&atilde;o expressa a ideia de que a reta &eacute; formada por uma sucess&atilde;o infinita de pontos alinhados, que seguem sempre a mesma dire&ccedil;&atilde;o.<\/p><p class=\"wp-block-paragraph\">Imagine-se no centro de uma rotat&oacute;ria e precisando chegar o mais r&aacute;pido poss&iacute;vel a uma cal&ccedil;ada reta que passa ao lado. O caminho mais curto ser&aacute; sempre em linha reta, formando um &acirc;ngulo de 90&deg; com a cal&ccedil;ada.<\/p><p class=\"wp-block-paragraph\">De maneira an&aacute;loga, ao analisar uma <strong>reta e uma <span id=\"urn:enhancement-4ffbd338-a80f-4c15-a236-d7ead9f6a96a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span><\/strong>, a <span id=\"urn:enhancement-77228781-3134-455f-8e22-caa0253696f5\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> <em>d <\/em>entre o centro da <span id=\"urn:enhancement-c6119d32-781d-4c0e-b6b0-075f3e49340c\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> e a reta &eacute; essencial para compreender a posi&ccedil;&atilde;o relativa entre as figuras.&nbsp;<\/p><p class=\"wp-block-paragraph\">Essa <span id=\"urn:enhancement-5bea6a48-afa1-47df-9add-e8d2c1ebc9f9\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> corresponde ao <strong>menor caminho poss&iacute;vel<\/strong> entre o ponto C e qualquer ponto da reta, ou seja, ao comprimento do segmento perpendicular que liga o centro da <span id=\"urn:enhancement-6c4b5b39-4c4c-44a5-b788-869f6966aa59\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> &agrave; reta.&nbsp;<\/p><p class=\"wp-block-paragraph\">Para encontrar o valor de <strong><em>d<\/em><\/strong>, utilizamos uma f&oacute;rmula espec&iacute;fica da geometria anal&iacute;tica para calcular a <span id=\"urn:enhancement-e16cbb5b-aed3-4c0d-9cb3-4e9b0fe87727\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> entre um ponto e uma reta. Dado um ponto (centro da <span id=\"urn:enhancement-060896ea-f4bd-4e78-8d5f-72e39f627506\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> neste caso) com coordenadas C(x0&#8203;,y0&#8203;) e uma reta na <span id=\"urn:enhancement-5e10b22c-10af-4f38-b34f-e7b23de5b004\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> <strong>ax+by+c=0<\/strong>. Temos que:<\/p><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"245\" height=\"98\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-71.png\" alt=\"\" class=\"wp-image-145696\"><\/figure><p class=\"wp-block-paragraph\">O <strong>numerador<\/strong> representa o valor absoluto do resultado obtido ao substituir as coordenadas do centro (x0,y0) na equa&ccedil;&atilde;o da reta, garantindo que a <span id=\"urn:enhancement-15355b19-a898-4fda-8497-e783fb46e986\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> seja sempre positiva. J&aacute; o <strong>denominador<\/strong> corresponde &agrave; raiz quadrada da soma dos quadrados dos coeficientes a e b da reta.<\/p><h2 class=\"wp-block-heading\" id=\"h-retas-e-numero-de-interseccoes\"><span class=\"ez-toc-section\" id=\"Retas-e-numero-de-interseccoes\"><\/span>Retas e n&uacute;mero de intersec&ccedil;&otilde;es<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-reta-secante\">Reta secante<\/h3><p class=\"wp-block-paragraph\">Imagine uma pizza perfeitamente redonda sobre uma mesa. Se voc&ecirc; pegar uma faca e fizer um corte reto que atravesse a pizza, a linha do seu corte representa uma <strong>reta secante<\/strong>. Ela entra por um lado e sai pelo outro. &Eacute; exatamente essa a ideia <span id=\"urn:enhancement-dfd3541f-a3a6-4c0d-82c2-eaa25602e317\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geom&eacute;trica<\/span>.&nbsp;<\/p><p class=\"wp-block-paragraph\">Uma reta &eacute; classificada como <strong>secante<\/strong> a uma <span id=\"urn:enhancement-561f4c00-c33e-499d-a95a-695c33ec6fe2\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> quando sua trajet&oacute;ria a leva a cruzar o interior da <span id=\"urn:enhancement-952a7184-e780-4780-84bf-17622bc13efd\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Essa &ldquo;invas&atilde;o&rdquo; do espa&ccedil;o interno da <span id=\"urn:enhancement-1484fd2d-f579-4fb6-a444-42ab979116a6\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> resulta na exist&ecirc;ncia de <strong><span id=\"urn:enhancement-10a050a9-8fd1-4b69-8697-640b7004b16a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/dois-pontos\">dois pontos<\/span> distintos<\/strong> que pertencem tanto &agrave; reta quanto &agrave; <span id=\"urn:enhancement-01834885-2682-4306-b89d-3927b6293617\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>.<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"650\" height=\"528\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-75.png\" alt=\"\" class=\"wp-image-145703\" style=\"width:266px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Esses <strong><span id=\"urn:enhancement-ba890bde-73d6-4d16-9416-c6b16ee69496\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/dois-pontos\">dois pontos<\/span><\/strong> (interse&ccedil;&atilde;o), vamos cham&aacute;-los de P1&#8203; e P2&#8203;, definem um segmento de reta muito importante: a <strong>corda<\/strong>. Toda reta secante, ao cruzar uma <span id=\"urn:enhancement-744c7afc-56d8-41ca-8a18-fbaf89b29585\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>, gera uma corda interna a ela.<\/p><p class=\"wp-block-paragraph\">Se a menor <span id=\"urn:enhancement-7a5479ab-5e66-45bc-8185-59cca741b595\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> da reta ao centro (d) &eacute; <strong>menor<\/strong> que a <span id=\"urn:enhancement-9432002c-68ca-4fc3-99bf-e7ed8f7f7666\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> da fronteira ao centro (r), isso significa que a reta <strong>obrigatoriamente<\/strong> passou por dentro da &aacute;rea delimitada pela <span id=\"urn:enhancement-20d22e44-3960-4dbe-aa9b-a994a576ba29\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Se ela entrar na &aacute;rea, ela ter&aacute; que sair, e &eacute; nesse trajeto de entrada e sa&iacute;da que os <span id=\"urn:enhancement-e2914346-5b02-429d-ba0c-8ba749be48b4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/dois-pontos\">dois pontos<\/span> de interse&ccedil;&atilde;o s&atilde;o criados.<\/p><h3 class=\"wp-block-heading\" id=\"h-reta-tangente\">Reta Tangente<\/h3><p class=\"wp-block-paragraph\">A reta tangente &eacute; um caso especial da rela&ccedil;&atilde;o entre uma reta e uma <span id=\"urn:enhancement-5e86cee6-b6ee-4e95-8459-959b98cdbc13\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. Ela acontece quando a reta toca a <span id=\"urn:enhancement-31fb927e-2263-4f5a-b331-3cd75271f3ee\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> em um &uacute;nico ponto, chamado ponto de tang&ecirc;ncia.<\/p><p class=\"wp-block-paragraph\">Para a reta ser tangente, &eacute; preciso que a <strong><span id=\"urn:enhancement-1df928e2-1d6e-4602-a36f-851271026575\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> entre o centro da <span id=\"urn:enhancement-1f0ee151-941a-4eea-b5d5-8aa1a40e2665\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> e a reta seja exatamente igual &agrave; do raio<\/strong>. Essa condi&ccedil;&atilde;o garante que a reta n&atilde;o corte e nem fique afastada, mas apenas toque a curva.<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"635\" height=\"564\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-76.png\" alt=\"\" class=\"wp-image-145704\" style=\"width:319px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">A <strong>propriedade fundamental da tangente<\/strong> diz que: o <strong>raio que liga o centro da <span id=\"urn:enhancement-5e9fd885-9f6c-468a-b16e-3610d5d3ec58\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> ao ponto de tang&ecirc;ncia &eacute; sempre perpendicular (<span id=\"urn:enhancement-d6cc6256-971f-4dea-bcef-dfc7af304468\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">forma<\/span> um &acirc;ngulo de 90&deg;) &agrave; reta tangente<\/strong>.&nbsp;<\/p><p class=\"wp-block-paragraph\">Essa rela&ccedil;&atilde;o &eacute; extremamente &uacute;til em problemas de <span id=\"urn:enhancement-c4726849-455a-4952-95b9-312a14da88e1\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/geometria\">geometria<\/span>, pois permite aplicar conceitos de &acirc;ngulos, ortogonalidade, tri&acirc;ngulos e at&eacute; equa&ccedil;&otilde;es da reta no <span id=\"urn:enhancement-9b23ad18-d70f-45d2-b23f-045bac304171\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano-cartesiano\">plano cartesiano<\/span>.<\/p><h3 class=\"wp-block-heading\" id=\"h-reta-externa\">Reta externa<\/h3><p class=\"wp-block-paragraph\">Uma reta &eacute; classificada como <strong>exterior<\/strong> (ou externa) a uma <span id=\"urn:enhancement-fe3b2139-a779-4007-a9ba-5fb51051f6f4\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> quando elas <strong>n&atilde;o possuem nenhum ponto em comum<\/strong>, ou seja, elas nunca se tocam. A reta e a <span id=\"urn:enhancement-4efd7e02-60dc-4f87-80e2-3b16c44140fa\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> s&atilde;o figuras completamente disjuntas no <span id=\"urn:enhancement-f1722e72-46f1-4b9c-b6bd-19ae17c67631\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano\">plano<\/span>; n&atilde;o h&aacute; um &uacute;nico ponto que satisfa&ccedil;a a equa&ccedil;&atilde;o da reta e a equa&ccedil;&atilde;o da <span id=\"urn:enhancement-ed623802-23c9-4ba3-a6e3-764477e6e25e\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> simultaneamente.&nbsp;<\/p><figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"703\" height=\"569\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-72.png\" alt=\"\" class=\"wp-image-145700\" style=\"width:326px;height:auto\"><\/figure><p class=\"wp-block-paragraph\">Se a menor <span id=\"urn:enhancement-6c35afc6-beba-4e37-8c75-9e949ceb6190\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> que a reta atinge em rela&ccedil;&atilde;o ao centro (d) j&aacute; &eacute; maior do que a <span id=\"urn:enhancement-5bd385bf-bdf2-49d8-a882-195ebfdb9e18\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/distancia\">dist&acirc;ncia<\/span> necess&aacute;ria para tocar a borda da <span id=\"urn:enhancement-a62c9c08-cdfe-42fe-a278-94a503417659\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span> (r), ent&atilde;o &eacute; imposs&iacute;vel que qualquer ponto da reta toque ou cruze a <span id=\"urn:enhancement-949da7a6-5215-4be1-8429-2bf436de0629\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncia<\/span>. O ponto de maior aproxima&ccedil;&atilde;o da reta j&aacute; est&aacute; longe demais, e todos os outros pontos da reta estar&atilde;o ainda mais distantes.<\/p><h2 class=\"wp-block-heading\" id=\"h-visao-geral\"><span class=\"ez-toc-section\" id=\"Visao-geral\"><\/span>Vis&atilde;o geral<span class=\"ez-toc-section-end\"><\/span><\/h2><figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"895\" height=\"263\" src=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-77.png\" alt=\"\" class=\"wp-image-145705\" srcset=\"https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-77.png 895w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-77-768x226.png 768w, https:\/\/vestibulares.estrategia.com\/portal\/wp-content\/uploads\/2025\/09\/image-77-800x235.png 800w\" sizes=\"(max-width: 895px) 100vw, 895px\" \/><\/figure><p class=\"wp-block-paragraph\"><\/p><h2><span class=\"ez-toc-section\" id=\"Questoes-sobre-posicao-relativa-entre-circunferencia-e-reta\"><\/span>Quest&otilde;es sobre posi&ccedil;&atilde;o relativa entre circunfer&ecirc;ncia e reta<span class=\"ez-toc-section-end\"><\/span><\/h2><h3 class=\"wp-block-heading\" id=\"h-simulado-usp-fuvest-2021\">Simulado USP &ndash; FUVEST (2021)<\/h3><p class=\"wp-block-paragraph\">Duas <span id=\"urn:enhancement-a110d8a2-3462-46ac-aa54-2b2b5dce43b1\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncias<\/span> &#120582;&#8321; e &#120582;&#8322; com raios 2 e 4 t&ecirc;m centros no primeiro quadrante do <span id=\"urn:enhancement-8d9c91fe-f019-4573-aa73-bbbf67632753\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/plano-cartesiano\">plano cartesiano<\/span>. Elas tangenciam Ox e Oy. Sabendo que as <span id=\"urn:enhancement-5356c6a9-8e37-4d2e-9d67-1b737898531a\" class=\"textannotation disambiguated wl-thing\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/circunferencia\">circunfer&ecirc;ncias<\/span> s&atilde;o secantes nos pontos (&#119909;&#8321;,&#119910;&#8321;) e (&#119909;&#8322;,&#119910;&#8322;). O valor de (&#119909;&#8321;+&#119910;&#8321;)&sup2;+(&#119909;&#8322;+&#119910;&#8322;)&sup2; &eacute;<\/p><p class=\"wp-block-paragraph\"><strong>A)<\/strong> 16<br><strong>B) <\/strong>9<br><strong>C)<\/strong> 18<br><strong>D)<\/strong> 12<br><strong>E)<\/strong> 24<\/p><details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary><strong>Resposta<\/strong><\/summary>\n<p class=\"wp-block-paragraph\">Alternativa correta: <strong>C<\/strong><\/p>\n<\/details><p class=\"wp-block-paragraph\"><\/p><p class=\"wp-block-paragraph\"><\/p><h2 class=\"wp-block-heading\" id=\"h-alcance-a-aprovacao-com-o-estrategia-vestibulares\"><span class=\"ez-toc-section\" id=\"Alcance-a-aprovacao-com-o-Estrategia-Vestibulares\"><\/span>Alcance a aprova&ccedil;&atilde;o com o Estrat&eacute;gia Vestibulares!<span class=\"ez-toc-section-end\"><\/span><\/h2><p class=\"wp-block-paragraph\">No <strong>Estrat&eacute;gia Vestibulares<\/strong>, voc&ecirc; encontra a prepara&ccedil;&atilde;o completa para conquistar sua aprova&ccedil;&atilde;o: materiais atualizados, professores especializados, tecnologia de ponta e um m&eacute;todo que j&aacute; transformou a vida de milhares de estudantes.&nbsp;<\/p><p class=\"wp-block-paragraph\">Se o seu sonho &eacute; passar no <span id=\"urn:enhancement-115c847f-e533-4b5e-b833-b9c312c51c27\" class=\"textannotation disambiguated wl-creative-work\" itemid=\"https:\/\/data.wordlift.io\/wl110249\/entity\/exame-nacional-do-ensino-medio-2\">Enem<\/span> ou no vestibular mais concorrido do pa&iacute;s, aqui voc&ecirc; tem tudo o que precisa para chegar l&aacute; com confian&ccedil;a e resultados reais.<\/p><p class=\"wp-block-paragraph\">Clique no banner e comece agora mesmo!<\/p><p class=\"wp-block-paragraph\"><a id=\"cta\" class=\"cta-imagem\" href=\"https:\/\/vestibulares.estrategia.com\/cursos\/\" target=\"blank\">\n                <img decoding=\"async\" width=\"100%\" 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