{"id":8364,"date":"2021-11-20T22:53:26","date_gmt":"2021-11-20T17:23:26","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8364"},"modified":"2022-01-31T18:04:48","modified_gmt":"2022-01-31T12:34:48","slug":"what-is-the-length-of-tangent-to-a-circle-formula-from-an-external-point","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-length-of-tangent-to-a-circle-formula-from-an-external-point\/","title":{"rendered":"Length of Tangent to a Circle Formula From an External Point"},"content":{"rendered":"

Here you will learn what is the length of tangent to a circle formula from an external point with example.<\/p>\n

Let’s begin –<\/p>\n

Length of Tangent to a Circle Formula<\/h2>\n

The length of tangent drawn from point (\\(x_1,y_1\\)) outside the circle<\/p>\n

S = \\(x^2 + y^2 + 2gx + 2fy + c\\) = 0 is,<\/p>\n

\\(\\sqrt{S_1}\\) = (\\(\\sqrt{{x_1}^2 + {y_1}^2 + 2gx_1 + 2fy_1 + c}\\))<\/p><\/blockquote>\n

Note<\/strong> : When we use this formula the coefficient of \\(x^2\\) and \\(y^2\\) must be 1.<\/p>\n

Also Read<\/strong> : Equation of Pair of Tangents to a Circle<\/a><\/p>\n

Example<\/strong><\/span> : Find the length of tangent from the point (9, 12) to the circle \\(2x^2 + 2y^2 – 6x + 8y + 10\\) = 0<\/p>\n

Solution<\/strong><\/span> : Dividing the given equation of circle by 2, we get the standard form,<\/p>\n

\\(x^2 + y^2 – 3x + 4y + 5\\) = 0<\/p>\n

Now, by using above formula the length from (9, 12) is<\/p>\n

\\(\\sqrt{9^2 + 12^2 + (-3)(12) + 4(9) + 10}\\) = \\(\\sqrt{81 + 144 – 36 + 36 +10}\\) = \\(\\sqrt{235}\\).<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the length of tangent to a circle formula from an external point with example. Let’s begin – Length of Tangent to a Circle Formula The length of tangent drawn from point (\\(x_1,y_1\\)) outside the circle S = \\(x^2 + y^2 + 2gx + 2fy + c\\) = 0 is, …<\/p>\n

Length of Tangent to a Circle Formula From an External Point<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[23],"tags":[844,842,841,843],"yoast_head":"\nLength of Tangent to a Circle Formula From an External Point<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the length of tangent to a circle formula from an external 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