Answer the following questions related to chords and central angles of a circle.
(a) Define a chord of a circle.
(b) Define a central angle of a circle.
(c) State the theorem that relates equal chords to the central angles they subtend at the centre and also state its converse.
(d) Using only the theorem stated in part (c), explain why, in a circle with centre O, if ∠AOB=∠COD, then AB=CD.
(e) Would the result obtained in part (d) remain true if the equal angles were subtended at any point on the circumference instead of at the centre? Give a reason for your answer.