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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 of $PQ$ is :

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\sqrt{112} cm

\sqrt{113} cm

\sqrt{85} cm

\sqrt{119} cm

answer is D.

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Detailed Solution

From the question we have,
Radius

OP = 5 cm

and

OQ = 12 cm

PQ

is the tangent to the circle.

∠ OPQ = 90^{\circ}

So,by Pythagoras theorem we get,

{PQ}^{2} = {OQ}^{2} - {OP}^{2}

\Rightarrow {PQ}^{2} = 12^{2} - 5^{2}

\Rightarrow {PQ}^{2} = 144 - 25

\Rightarrow {PQ}^{2} = 119

PQ = \sqrt{119} cm

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