Question

From a point $P$ which is at a distance of $13$ cm from the centre $O$ of a circle of radius $5$ cm, the pair of tangents $PQ$ and $PR$ to the circle are drawn. Then the area of the quadrilateral $PQOR$ is:

• A. $60$ cm${}^2$
• B. $65$ cm${}^2$
• C. $30$ cm${}^2$
• D. $32.5$ cm${}^2$

Answer 1

Answer: (A)

$60$ cm${}^2$

The radius perpendicular tangent at the pt. of contact, therefore, $OQ\perp PQ$ and $OR\perp PR$
In rt. $△OPQ$, we have
$PQ=\sqrt{O{P}^2-O{Q}^2}$
$=\sqrt{169-25}=\sqrt{144}=12$ cm
$\Rightarrow$ $PR=12$ cm (Two tangents from the same external pt. to a circle are equal)
Now area of quad. $PQOR=2\times$Area of $△POQ$
$=(2\times \frac{1}{2}\times 12\times 5)$ cm${}^2=60$ cm${}^2$