Question

3. 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

​

Answer 1

Explanation:

In the above figure, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ.

And so, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ we get,

OQ² = OP² +PQ²

↪(12)² = 5² + PQ²

↪PQ² = 144 - 25

↪PQ² = 119

↪PQ = √119 cm

So, option D i.e. √119 cm is the length of PQ.