{"id":9878,"date":"2022-01-31T19:26:52","date_gmt":"2022-01-31T13:56:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9878"},"modified":"2022-01-31T19:27:57","modified_gmt":"2022-01-31T13:57:57","slug":"chord-of-contact-of-circle-length-and-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/chord-of-contact-of-circle-length-and-equation\/","title":{"rendered":"Chord of Contact of Circle – Length and Equation"},"content":{"rendered":"

Here you will learn equation of chord of contact of circle and length of chord of contact of circle.<\/p>\n

Let’s begin –<\/p>\n

Equation of Chord of Contact<\/h2>\n

A line joining the two points of contacts of two tangents drawn from a point outside the circle, is called chord of contact of that point.<\/p>\n

\"chord<\/p>\n

If two tangents \\(PT_1\\) and \\(PT_2\\) are drawn from the point P\\((x_1, y_1)\\) to the circle S = \\(x^2 + y^2 + 2gx + 2fy + c\\) = 0,<\/p>\n

then the equation of the chord of contact \\(T_1T_2\\) is :<\/p>\n

\\(xx_1 + yy_1 + g(x + x_1) + f(y + y_1) + c\\) = 0<\/p>\n

i.e. T = 0 same as equation of tangent<\/p><\/blockquote>\n

Also Read : Length of Tangent to a Circle Formula From an External Point<\/a><\/p>\n

Length and Angle Formula :<\/h2>\n

The formula for length is \\(T_1T_2\\) = \\(2LR\\over \\sqrt{R^2 + L^2}\\).<\/p>\n

The formula for Angle between the pair of tangents from P\\((x_1, y_1)\\) = \\(tan^{-1}({2RL\\over L^2 – R^2})\\).<\/p><\/blockquote>\n

Area of the Triangle Formed by Pair of Tangents Formula<\/h2>\n

The area of the triangle formed by the pair of the tangents and its chord of contact is given by the formula<\/p>\n

\\(RL^3\\over R^2 + L^2\\)<\/p><\/blockquote>\n

Where R is the radius of the circle and L is the length of the tangent from \\((x_1, y_1)\\) on S = 0<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn equation of chord of contact of circle and length of chord of contact of circle. Let’s begin – Equation of Chord of Contact A line joining the two points of contacts of two tangents drawn from a point outside the circle, is called chord of contact of that point. If two …<\/p>\n

Chord of Contact of Circle – Length and Equation<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[23],"tags":[848,850,849],"yoast_head":"\nChord of Contact of Circle - Length and Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn equation of chord of contact of circle and length of chord of contact of circle.\" \/>\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\/chord-of-contact-of-circle-length-and-equation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Chord of Contact of Circle - 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