Two external points and lie on the same straight line through the centre of a circle

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

Two external points

P

and

Q

lie on the same straight line through the centre

O

of a circle, with

Q

being farther from

O

than

P

. The distance

OP

15\,\text{cm}

, and the tangent drawn from

P

to the circle is

9\,\text{cm}

long. The tangent drawn from

Q

to the same circle is

12\,\text{cm}

long. (i) Find the radius of the circle. (ii) Determine the distance

OQ

. (iii) Calculate the length

PQ