Question

If the angle between two tangents drawn from an external point P to a circle of radius 'a' and centre O, is ${60}^0$, then find the length of OP.

Answer 1

$\angle QPR={90}^{\circ }$

and $\angle OPQ={30}^{\circ }$

$\sin {30}^{\circ }=\frac{OQ}{OP}⟹OP=\frac{OQ}{\sin {30}^{\circ }}=\frac{a}{1/2}=2a$

$OP=2a$ units.