Two tangents AP and AQ are drawn to a circle with center O from an external point A, where P and Q are points on the circle.  If ∠PAQ = 80°, then ∠AOP is equal to?

60° 75° 85° 50°

50°

∠PAQ = 80°, and ∠P and ∠Q = 90°  In the case of tangent ⇒ line OA bisect the angles ∠PAQ and ∠POQ. Therefore, In Δ PAO: ∠P = 90°, ∠PAO = 40°, so ∠PAO = 90° - 40° = 50°