Question

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

(A) 12 cm. (B) 13 cm (C) 8.5 cm (D) cm

Answer 1

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

OP PQ

By applying Pythagoras theorem in ΔOPQ,

OP² + PQ² = OQ²

5² + PQ² =12²

PQ² =144 − 25

PQ = cm.

Hence, the correct answer is (D).