The tangent at a point P of a circle with centre 'O' intersects the diameter XY of the circle when extended at the point T. If ∠TPY = 15°, then find ∠PXY.

15°

∠XPT = ∠XPY + ∠TPY [∠XPY = 90° angle made by diameter]

∠XPT = 90° + 15° = 105°

Now, OP is radius so it made 90° angle with tangent ∠OPT = 90°

Now, ∠XPO = ∠XPT - ∠OPT = 105° - 90° = 15°

As, OP = OX ⇒ ∠OPX - ∠OXP = 15°

 ⇒ ∠PXY = 15°