Mathematics

Problem

A circle with centre

O

and radius

5\,\text{cm}

is given. Three points

P,\;Q

and

R

lie on the ray

OA

such that

OP = 3\,\text{cm}

OQ = 5\,\text{cm}

and

OR = 8\,\text{cm}

. a. (i) For each of the points

P,\;Q

and

R

, state whether it lies inside the circle, on the circle or outside the circle. b. (ii) For each point, state the exact number of tangents that can be drawn to the circle and give a reason for your answer. c. (iii) If

S

is a point such that

OS=x\,\text{cm}

, 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.

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