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Question

A tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q so that OQ=12cm. Length PQ is :


A

12cm

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B

13cm

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C

8.5cm

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D

119cm

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Solution

The correct option is D

119cm


Step 1. From the figure, the line that is drawn from the centre of the given circle to the tangentPQ is perpendicular to PQ

So, OPPQ

Step 2. Using Pythagoras theorem in right angled triangle OPQ we have,

OQ2=OP2+PQ2122=52+PQ2144=25+PQ2144-25=PQ2119=PQ2PQ2=119PQ=119

Hence option (D) is the correct option.


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