• # question_answer 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.

 Given,   $\angle APB=60{}^\circ$ $\Rightarrow$ $\angle APO=30{}^\circ$ In right angle$\Delta \text{ O}AP$, $\frac{OP}{OA}=\cos ec\,\,30{}^\circ$ $\frac{OP}{a}=2\Rightarrow OP=2a$