Question

A circle with radius 12cm , from a point P which is 20 cm away from the centre then length of tangent is

Answer 1

$\red{ \large{ \underline{ \bold{tangent = 16cm}}}}$

let the tangent be PQ with point of contact as Q and the center of the circle be O

by pythagoras theorem we get:-

$\blue{ {hypotenuse}^{2} } = \green{ {base}^{2} + {hight}^{2} }$

$\blue{ {PO}^{2} } = \green{ {PQ}^{2} + {QO}^{2} }$

$\blue{ {(20)}^{2} } = \green{ {tangent}^{2} + {(12)}^{2} }$

$\blue{400} - \green{144} = \green{ {tangent}^{2} }$

$\green{tangent} = \orange{ \sqrt{256} }$

$\green{tangent} = \orange{16cm}$