Question

O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then, the area of quadrilateral PQOR is


(a) 60 cm²
(b) 32.5 cm²
(c) 65 cm²
(d) 30 cm²

Answer 1

(a) 60 cm²
Given,$OQ=OR=5cm,OP=13$ cm.

$\angle OQP=\angle ORP={90}^0$

(Tangents drawn from an external point are perpendicular to the radius at the point of contact)

From right-angled

$\Delta POQ:P{Q}^2=O{P}^2-O{Q}^2$

$\Rightarrow P{Q}^2={13}^2-5^2$

$\Rightarrow P{Q}^2=144$

$\Rightarrow PQ=12cm$

$\therefore \text{Area of}△OQP=12\times PQ\times OQ$

$=12\times 12\times 5c{m}^2$

$=30c{m}^2$

Similarly, $\text{Area of}△ORP=30c{m}^2$

∴arquad. $PQOR=30+30c{m}^2=60c{m}^2$