Question

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

• A. $12cm$
• B. $\sqrt{163}cm$
• C. $\sqrt{119}cm$
• D. None of these

Answer 1

Answer: (C)

$\sqrt{119}cm$

The radius of the circle $=5cm$

$OQ=12cm$

$\angle OPQ={90}^o$ [ The tangent to a circle is perpendicular to the radius through the point of contact]

$P{Q}^2=O{Q}^2-O{P}^2$ [ By Pythagoras theorem]

$P{Q}^2={12}^2-5^2=144-25=119$

$PQ=\sqrt{119}cm$