Answer all parts of the question.
(i) State and prove the theorem: "In a circle, equal chords are equidistant from the centre."
(ii) Prove the converse of the theorem stated in part (i).
(iii) A circle has radius 13cm. Two of its chords AB and CD are equal and each is at a perpendicular distance of 5cm from the centre O. Find the common length of the chords.