Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q such that OQ = 13 cm. Length PQ is ______ 

Options

• `sqrt119`

• 8.5 cm

• 13 cm

• 12 cm

Answer 1

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q such that OQ = 13 cm. Length PQ is 12 cm.

Explanation:

Given that OP = 5 cm, OQ = 13 cm

To find PQ.

Applying Pythagoras theorem to triangle OPQ

OP² + QP² = OQ²

5² + QP² = 13²

QP² = 169 - 25 = 144

QP = `sqrt144` cm

QP = 12 cm