Consider a line segment AB. Points C and D lie on the same side of AB such that ∠ACB=∠ADB.
a. (i) State the theorem that relates equal angles subtended by a chord at points on the circumference of a circle.
b. (ii) Using the theorem stated in part (i), explain whether the four points A, B, C and D must lie on a single circle.
c. (iii) Give one reason why the condition that C and D are on the same side of AB is necessary for the conclusion reached in part (ii).