PQ is a tangent to a circle with centre O at point P. If ΔOPQ is an isosceles triangle where OP = PQ, then ∠OQP is equal to:
1 mark
🔍 View Detailed Solution & Schema →

Question

PQ is a tangent to a circle with centre O at point P. If ΔOPQ is an isosceles triangle where OP = PQ, then ∠OQP is equal to:

Accepted Answer

Angle at P is 90° because radius OP is perpendicular to tangent PQ. Since OP = PQ, the angles opposite to them are equal, i.e., ∠POQ = ∠OQP. In ΔOPQ, ∠OPQ + ∠POQ + ∠OQP = 180° ⇒ 90° + 2∠OQP = 180° ⇒ 2∠OQP = 90° ⇒ ∠OQP = 45°.

Circles

❓ Sibling Questions in this Chapter