Two tangents are drawn from a point $mathrm{P}$ to a circle at $mathrm{A}$ and $mathrm{B}$. $mathrm{O}$ is the centre of the circle. If $angle$ AOP $=60^{circ}$, then $angle mathrm{APB}$ is

Answer : Option D

Explanation :

In right ’s OAP and OPB,

AP = PB , OA = OB

OP = OP

OP = OP

∴ ΔOAP ≅ ΔOPB

∴ ∠AOP = ∠POB and ∠APO

= ∠ OPB

From Δ AOP,

From Δ AOP,

∠ APO = 180° – 90° – 60° = 30°

∴ ∠ APB = 2 × 30 = 60°