Question

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

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

Answer 1

Answer: (A)

$60c{m}^2$

Tangent $PQ$ and $PR$ are perpendicular to $OQ$ and $OR$ respectively.

Hence both triangles $POQ$ and $PQR$ are right angled.

$PQ=$ $\sqrt{(OP{)}^2-(OQ{)}^2}$

$=$ $\sqrt{(13{)}^2-(5{)}^2}$

$=$ $12$ cm

Area of $△POQ=\frac{1}{2}\times PQ\times OQ$

$=$ $\frac{1}{2}\times 12\times 5$

$=$ $30c{m}^2$

Similarly, area of $△POR=\frac{1}{2}\times PR\times OR$

$=$ $\frac{1}{2}\times 12\times 5$

$=$ $30c{m}^2$

Area of quadrilateral $PQOR=$ $30+30$

$=$ $60c{m}^2$