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 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:

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

As a result, OP ⊥ PQ

In triangle ΔOPQ, using Pythagoras theorem we get,

OQ2 = OP2+PQ2

(12)= 52+PQ2

PQ2 = 144-25

PQ2 = 119

PQ = √119 cm

As a result, option D is the correct answer i.e. length of PQ is √119 cm.