Consider a circle with centre O and two chords AB and CD. Answer the following questions.
a. (i) Define (a) a chord and (b) a central angle of a circle.
b. (ii) State the relationship between equal chords and the angles subtended by them at the centre.
c. (iii) If AB=CD, prove that ∠AOB=∠COD.
d. (iv) Conversely, if ∠AOB=∠COD, prove that AB=CD. Explain your reasoning clearly.