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 quad. PQOR is ______.

Options

• 60 cm²

• 32.5 cm²

• 65 cm²

• 30 cm²

Answer 1

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 quad. PQOR is 60 cm².

Explanation:

Clearly, OQ = OR = 5 cm, ∠OQP = ∠ORP = 90° and OP = 13 cm.

∴ PQ² = OP² – OQ²

= (13)² – (5)² 

= 169 – 25 

= 144

⇒ PQ = `sqrt(144)` 

⇒ PQ = 12 cm

∴ `ar(ΔOQP) = 1/2 xx PQ xx OQ`

= `(1/2 xx 12 xx 5) cm^2`

= 30 cm²

Similarly, ar(ΔORP) = 30 cm².

∴ ar(quad. PQOR) = (30 + 30) cm²

= 60 cm²