In a circle with centre O, two chords AB and CD are such that AB=CD.
a. (i) Prove that ∠AOB=∠COD.
b. (ii) If the measure of the minor arc AB is 80∘, find the measure of the minor arc CD.
c. (iii) Suppose the chord CD is moved closer to the centre so that its perpendicular distance from O becomes less than that of AB. Will CD still remain equal to AB? Give a clear reason based on circle properties.