Question

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 $PQ$ is:

• A. $12$ cm
• B. $13$ cm
• C. $8.5$ cm
• D. $\sqrt{119}$ cm

Answer 1

The correct option is D $\sqrt{119}$ cm

$OP=5$ cm and $OQ=12$ cm

To find: $PQ$

By using Pythagoras Theorem, we have

$O{P}^2+P{Q}^2=O{Q}^2$

Putting given values in above equation

$5^2+P{Q}^2={12}^2$
$⟹P{Q}^2=144-25$
$⟹P{Q}^2=119$
$PQ=\sqrt{119}$ cm