Question

The tangents drawn at the point P and Q of a circle centred at O meet at A. If ∠POQ = 120°, then what is the ratio of ∠PAQ : ∠PAO?

• A. 2 : 3
• B. 4 : 1
• C. 2 : 1
• D. 5 : 2

Answer 1

Answer:

C. 2 : 1

∠APO = 90 and ∠OQA = 90° ∠POQ = 120° (given) In quadrilateral POQA, ∠POQ + ∠PAQ + ∠APO + ∠OQA = 360° ∠PAQ = 60° in triangle POA, ∠PAO = 30° -∠PAQ = 2∠PAO