{"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
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
<\/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