{"id":4008,"date":"2021-08-13T18:18:28","date_gmt":"2021-08-13T18:18:28","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4008"},"modified":"2021-11-30T16:29:32","modified_gmt":"2021-11-30T10:59:32","slug":"formula-for-circumcenter-of-a-triangle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/","title":{"rendered":"Formula for Circumcenter of a Triangle | Incenter of Triangle"},"content":{"rendered":"

Here, you will learn formula for circumcenter of a triangle and formula for incenter of a triangle.<\/p>\n

Let’s begin –<\/p>\n

Formula for Circumcenter of a Triangle<\/h2>\n

It is the point of intersection of perpendicular bisectors of the sides of a triangle. If O is the circumcenter of any triangle ABC, then \\(OA^2\\) = \\(OB^2\\) = \\(OC^2\\). Also it is the center of circle touching all the vertices of a triangle.<\/p>\n

Note :<\/strong><\/p>\n

\n

(i)\u00a0 If the triangle is right angled, then its circumcenter is the mid-point of the hypotenuse.<\/p>\n

(iii)\u00a0 The Co-ordinates of circumcenter is :<\/p>\n

Circumcenter = (\\(x_1sin2A+x_2sin2B+x_3sin2C\\over {sin2A+sin2B+sin2C}\\),\\(y_1sin2A+y_2sin2B+y_3sin2C\\over {sin2A+sin2B+sin2C}\\))<\/p>\n<\/blockquote>\n

Incenter of a Triangle<\/h2>\n

The incenter is the point of intersection of internal bisectors of the angles of a triangle. Also it is a centre of the circle touching all the sides of the triangle.<\/p>\n

\n

Co-ordinates of incenter I is (\\(ax_1+bx_2+cx_3\\over {a+b+c}\\),\\(ay_1+by_2+cy_3\\over {a+b+c}\\)) where a,b,c are the sides of the triangle ABC.<\/p>\n<\/blockquote>\n

Note :<\/strong><\/p>\n

(i)\u00a0 Angle bisector divides the opposite sides in the ratio of remaining sides e.g. \\(BD\\over DC\\) = \\(AB\\over AC\\) = \\(c\\over b\\)<\/p>\n

(ii)\u00a0 Incenter divides the angle bisectors in the ratio (b+c) : a, (c+a) : b, (a+b) : c.<\/p>\n

Remarks :<\/strong><\/p>\n

(i)\u00a0 If the triangle is equilateral, then centroid, incentre, orthocenter, circumcenter coincide.<\/p>\n

(ii)\u00a0 Orthocenter, centroid and circumcenter are always collinear and centroid divides the line joining orthocenter and circumcenter in the ratio 2 : 1.<\/p>\n

(iii)\u00a0 In an isosceles triangle centroid, incenter, orthocenter and circumcenter lie on the same line.<\/p>\n

Hope you learnt formula for circumcenter of a triangle and formula for incenter of a triangle. To learn more practice more question and get ahead in competition. Good Luck!<\/p>\n\n\n

\n
Next – Orthocenter in a Triangle | Equation of Locus<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Centroid in a Triangle \u2013 Formula and Example<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn formula for circumcenter of a triangle and formula for incenter of a triangle. Let’s begin – Formula for Circumcenter of a Triangle It is the point of intersection of perpendicular bisectors of the sides of a triangle. If O is the circumcenter of any triangle ABC, then \\(OA^2\\) = \\(OB^2\\) = …<\/p>\n

Formula for Circumcenter of a Triangle | Incenter of Triangle<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[32],"tags":[641,642],"yoast_head":"\nFormula for Circumcenter of a Triangle | Incenter of Triangle<\/title>\n<meta name=\"description\" content=\"In this post you will learn formula for circumcenter of a triangle and formula for incenter of a triangle.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Circumcenter of a Triangle | Incenter of Triangle\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn formula for circumcenter of a triangle and formula for incenter of a triangle.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-13T18:18:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-30T10:59:32+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Formula for Circumcenter of a Triangle | Incenter of Triangle\",\"datePublished\":\"2021-08-13T18:18:28+00:00\",\"dateModified\":\"2021-11-30T10:59:32+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\"},\"wordCount\":336,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"circumcenter of a triangle formula\",\"incenter of a triangle formula\"],\"articleSection\":[\"Straight Line\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\",\"url\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\",\"name\":\"Formula for Circumcenter of a Triangle | Incenter of Triangle\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-13T18:18:28+00:00\",\"dateModified\":\"2021-11-30T10:59:32+00:00\",\"description\":\"In this post you will learn formula for circumcenter of a triangle and formula for incenter of a triangle.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circumcenter-of-a-triangle\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Formula for Circumcenter of a Triangle | Incenter of Triangle\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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