Answer: A (30°)
Since OA ⊥ PA (radius ⊥ tangent), ∠OAP = 90°, so ∠OAB = 15° means ∠PAB = 90° − 15° = 75°. By symmetry ∠PBA = 75°, so ∠APB = 180° − 75° − 75° = 30°.
Key facts used: (1) Radius ⊥ tangent at point of contact (Theorem 10.1), so ∠OAP = 90°. (2) PA = PB (Theorem 10.2), so △PAB is isosceles. Since ∠OAB = 15°, ∠PAB = 90° − 15° = 75°; by symmetry ∠PBA = 75°; hence ∠APB = 180° − 150° = 30°. Examiners expect you to state both theorems clearly.