Question

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is ${60}^{\circ }$, then find the length of OP.

Answer 1

Given,

$\angle APB={60}^{\circ }$

$\angle APO={30}^{\circ }$[ $\because$ tangents drawn from an exterior point to a circle are equally inclined to each other.]



In right angle $△OAP$

$\frac{OP}{OA}=cosec{30}^{\circ }$

$\frac{OP}{a}=2\Rightarrow OP=2a$