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Question -

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at



Answer -

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

And so, OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ weget,

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.

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