Question

PQ and PR are tangents to the circle of radius 3 cm and centre O. If the length of each tangent is 4 cm, then the perimeter of ΔOQP is:

विकल्प

• 5 cm

• 12 cm

• 9 cm

• 8 cm

Answer 1

12 cm

Explanation:

Radius of the circle OQ = 3 cm

Length of tangent PQ = 4 cm

PQ is tangent to the circle at point Q.

Then ∠Q = 90°

In ΔOQP,

By Pythagorean theorem

⇒ (PQ)² + (OQ)² = (OР)²

⇒ (4)² + (3)² = (OP)²

⇒ 16 + 9 = (OР)²

⇒ (OP)² = 25

⇒ OP = `sqrt(25)`

⇒ OP = 5 cm

The perimeter of ΔOQP = PQ + OQ + OP

= 3 + 4 + 5

= 12 cm