In a circle with centre O, chords AB and CD are equal and intersect at right angles at point P inside the circle.
a. (i) Prove that ∠AOB=∠COD.
b. (ii) Prove that OP is the bisector of ∠AOC.
c. (iii) If OP=4cm and the radius of the circle is 10cm, calculate the length of each chord.