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. \(\sqrt {119}\) cm

Answer 1

The Correct Option is D

We know that \(PQ^2 =144 - 25\) the line drawn from the centre of the circle to the tangent is perpendicular to the tangent. 
∴ \(OP ⊥ PQ\)
By applying Pythagoras theorem in \(\text {ΔOPQ}\),

∴ \(OP^2 + PQ^2 = OQ^2\)
\(5^2 + PQ^2 =12^2\)
\(25 + PQ^2 =144\)
\(PQ^2 =144 - 25\)
\(PQ^2 =119\)
\(PQ = \sqrt {119}\  cm\)

Hence, the correct option is (D): \(\sqrt {119}\  cm\)