Question

The 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. Then the length of the tangent is

(A) 13 cm

(B) \(\sqrt{119}\)

(C) 14 cm

(D) 11 cm

Answer 1

Correct option is: (B)  \(\sqrt{119}\) cm.

\(\because\) OP \(\perp\) PQ (Radius and tangent are perpendicular at point of contact)

= \(\angle\) OPQ = 90°

Now, in right \(\triangle\) OPQ

\(PQ^2 = OQ^2 - OP^2 = 12^2 - 5^2 \)

= 144 - 25 = 119

\(\therefore\) PQ = \(\sqrt{119}\) cm

Hence, length of tangent PQ is \(\sqrt{119}\) cm.

Answer 2

Correct option is: (B) \(\sqrt{119}\)