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. What is the Length PQ?

Question

(A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm.

Answer 1

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴ OP ⊥ PQ

By Pythagoras theorem in ΔOPQ,

OQ² = OP² + PQ²
⇒ (12)² = 5² + PQ²

⇒PQ² = 144 - 25

⇒PQ² = 119

⇒PQ = √119 cm

So, (D) is the right option.