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 ______ 

Options

• 60 cm²

• 65 cm²

• 30 cm²

• 32.5 cm²

Answer 1

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 60 cm².

Explanation:

Firstly, draw a circle of radius 5 cm with 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.

∵ OQ ⊥ QP  ...[Since, QP is a tangent line]

In right angled ∆PQO,

OP² = OQ² + QP²

⇒ 13² = 5² + QP²

⇒ QP² = 169 – 25 = 144

⇒ QP = 12 cm

Now, area of ∆OQP

= `1/2 xx "QP" xx "QO"`

= `1/2 xx 12 xx 5`

= 30 cm²

∴ Area of quadrilateral PQOR

= 2 × ar ∆OQP

= 2 × 30

= 60 cm²