Two tangents AP and AQ are drawn to a circle with centre O from an external point A, where P and Q are points on the circle. If the ∠PAQ = 70°, then the ∠AOP is equal to:
Answer & explanation
Correct answer: option 3
We have,
∠PAQ = 70°
∠PAQ + ∠POQ + ∠OPA + ∠OQA = 360°
= 70° + ∠POQ + 90° + 90° = 360°
= ∠POQ = 360° - 70° - 90° - 90°
= ∠POQ = 110°
= ∠AOP = ∠AOQ = 110°/2
= ∠AOP = 55°