Let O be the centre of a circle and let AB be a chord of the circle. A point C lies on AB such that OC⊥AB. Prove the following statements.
(i) Show that C is the midpoint of AB.
(ii) Conversely, if C is the midpoint of chord AB, prove that OC is perpendicular to AB. Thus establish a necessary and sufficient condition relating a perpendicular from the centre and the midpoint of a chord.