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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)= 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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