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. 119 cm.

(D)

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

OP Ʇ PQ

By applying Pythagoras theorem in ΔOPQ,

OP² + PQ² = OQ²

5² + PQ² =12²

PQ² =144 - 25

PQ = cm.