Question

PT is a tangent to the circle at T. If ∠ ABC = 70° and ∠ ACB = 50° ; calculate : ∠ APT

Answer 1

Join AT and BT.

∠ BTX = ∠ TCB = 30° (Angles in the same segment)

∴ ∠ PTB = 180° - 30° = 150°

Now in Δ PTB ,

∠APT + ∠ PTB + ∠ ABT = 180°

⇒ ∠APT +  150° + 20° = 180°

⇒ ∠APT = 180° - 170° = 10°