From an external point P, two tangents PA and PB are drawn to a circle with centre O. The chord AB is also drawn.
a. (i) Prove that △OAP≅△OBP and hence show that OA=OB.
b. (ii) If ∠APB=60∘, find the measure of ∠AOB.
c. (iii) Is the quadrilateral AOBP cyclic? Give a reason for your answer.