In a circle with centre O, let AB and CD be two chords.
a. (i) Prove that the line segment drawn from the centre of a circle perpendicular to a chord bisects the chord.
b. (ii) Using the result of part (i), show that if two chords of a circle are equidistant from the centre, then they are equal in length.
c. (iii) Further, prove the converse: if two chords of a circle are equal in length, then they are equidistant from the centre.