If PA and PB tangents to a circle with center such that $$\angle APB$$=80° then $$\angle AOP$$ =

Given : $$\angle$$ APB = $$80^\circ$$

To find : $$\angle$$ AOP = $$\theta$$ = ?

Solution : $$\angle$$ APO = $$\frac{1}{2} \times$$ $$\angle$$ APB

=> $$\angle$$ APO = $$\frac{1}{2} \times 80^\circ=40^\circ$$

Also, the radius of a circle intersects the tangent at the circumference of circle at $$90^\circ$$

=> $$\angle$$ OAP = $$90^\circ$$

In $$\triangle$$ AOP

=> $$\angle$$ AOP + $$\angle$$ APO + $$\angle$$ OAP = $$180^\circ$$

=> $$\theta + 40^\circ+90^\circ=180^\circ$$

=> $$\theta=180^\circ-130^\circ$$

=> $$\theta=50^\circ$$

=> Ans - (B)