In a circle with centre O, AB and CD are two chords such that AB=CD.
a. (i) Explain why ∠AOB=∠COD. Give complete reasoning.
b. (ii) If ∠AOB=80∘, state the measure of the arc CD and justify your answer.
c. (iii) Let M and N be the mid-points of AB and CD respectively. Compare the lengths OM and ON and give reasons for your conclusion.