MNOP is a cyclic quadrilateral. The angle bisector of ∠PMN and ∠PON meets the circle at point A and B respectively

MNOP is a cyclic quadrilateral. The angle bisector of ∠PMN and ∠PON meets the circle at point A and B respectively. Find the value of ∠AMB?

(a) 45°

(b) 90°

(c) 60°

(d) 120°

Sol:

Assume any angle ∠PMN = 60°

Angle made by arc BN = 60° at

So angle made by arc BN = 60° at M

∴ ∠AMB = 90°