A,B,C and D are four successive points on a circle with centre O. The chords AB and CD are equal, and so are chords AD and BC. The chords AC and BD intersect at point P inside the circle. Carry out the following tasks:
(a) Prove that △APD is congruent to △BPC.
(b) Hence show that ∠APD=∠BPC.
(c) Deduce that ∠AOB=∠COD.