Question

In the figure, PA is a tangent from an external point P to the circle with centre O. If ∠POB = 110°, then the measure of ∠APO is:

• A. 40°
• B. 20°
• C. 25°
• D. 30°

Answer 1

Answer:

B. 20°

∠POB = 110° ∠POB + ∠POA = 180° [Straight line] ⇒ 110° + ∠POA = 180 ⇒ ∠POA = 180° - 110° = 70° ∠OAP = 90° [tangent at A] In ΔAPO ∠APO + ∠POA + ∠OAP = 180° ⇒ ∠APO + 70° + 90° = 180° ⇒ ∠APO = 180° - 90° - 70° = 20°