Question

PQ is a tangent to a circle with centre O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to ______.

विकल्प

• 30°

• 45°

• 60°

• 90°

Answer 1

PQ is a tangent to a circle with centre O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to 45°.

Explanation:

We have OP ⊥ PQ, i.e., ∠OPQ = 90°.

ΔOPQ is isosceles

⇒ OP = PQ

⇒ ∠OQP = ∠POQ   ...[∵ In a triangle, angles opposite equal sides are equal]

⇒ ∠OQP = 45°