Question

From a point P which is at a distance of 13 cm from the point 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 point 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:

OP² = OQ² + PQ²

169 = 25 + PQ²

PQ² = 144

PQ = 12

Area PQOR = ar(AOPQ) + ar(AOPR)
= `1/2 × 12 × 5 + 1/2 × 12 × 5` = 60 cm²

Answer 2

From a point P which is at a distance of 13 cm from the point 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 = `/2 xx QP xx QO`

= `1/2 xx 12 xx 5` = 30 cm²

∴ Area of quadrilateral PQOR = 2 × ar ∆OQP

= 2 × 30

= 60 cm²