In a circle with centre O and radius 8cm, a chord AB of length 10cm is drawn. A line OE is drawn from the centre perpendicular to AB, meeting AB at E.
a. (i) State the theorem that relates a line drawn from the centre of a circle perpendicular to a chord.
b. (ii) Prove that E is the mid-point of AB.
c. (iii) Calculate the length of OE. Show all required steps and justifications.