Question

From a point P which is at a distance 13 cm from the centre O of a circle of radious 5 cm , the pair of tangents PQ and PR to the circle are drawn . Then the area of the quadrilateral PQOR is
(a) 60 cm² (b) 65 cm² (c) 30 cm² (d) 32.5 cm²

Answer 1

Clearly tangent PQ and PR are perpendicular to OQ and OR respectively.
Hence both triangles POQ and PQR are right angled.
$P{Q}^2=O{P}^2-O{Q}^2={13}^2-5^2$

$PQ=12cm$
Area of $\Delta POQ=\frac{OQ\times PQ}{2}=\frac{5\times 12}{2}=30c{m}^2$
Similarly,
Area of $\Delta POR=$ Area of $\Delta POQ=30c{m}^2$ (Both the triangles are symmetrical)
Area of quadrilateral $PQOR=30+30=60c{m}^2$
Hence, the correct answer is option (a).