A circle with centre O and radius 5cm is given. Three points P,Q and R lie on the ray OA such that OP=3cm, OQ=5cm and OR=8cm.
(i) For each of the points P,Q and R, state whether it lies inside the circle, on the circle or outside the circle.
(ii) For each point, state the exact number of tangents that can be drawn to the circle and give a reason for your answer.
(iii) If S is a point such that OS=xcm, explain how the number of tangents that can be drawn from S to the circle depends on the value of x. Justify your conclusion carefully.