Let ABCD be a quadrilateral inscribed in a circle with centre O. Suppose that ∠AOB=∠COD.
(a) Prove that AB=CD.
(b) If it is further given that ∠ABC=∠CDA, show that AD∥BC.
(c) Using the results of parts (a) and (b), classify the quadrilateral ABCD and state your reasons clearly.