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 is 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

The correct option is (A) 60 cm${}^2$

Firstly, draw a circle of radius 5 cm having centre O . P is a point at a distance of 13 cm from O. A pair of tangents PQ and PR are drawn.

Thus, Quadrilateral PQOR is formed.
[Since , QP is a tangent line]
$\therefore OQ\perp QP$
In right angled $\Delta PQO,$
$O{P}^2=O{Q}^2+Q{P}^2\Rightarrow {13}^2=5^2+Q{P}^2\Rightarrow Q{P}^2=169-25=144QP=12cmNow,areaof\Delta OQP=\frac{1}{2}\times QP\times QO=\frac{1}{2}\times 12\times 5=30c{m}^2\therefore AreaofquadrilateralQORP=2\times Areaof\Delta OQP=2\times 30=60c{m}^2$