Question

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

Answer 1

Join AT and BT.

∠ CBA = 70°

∴ ∠ABT = ∠CBT - ∠CBA = 90° - 70° = 20°

Now , ∠ ACT = ∠ABT = 20°  (Angles the same segment of the circle)

∴ ∠TCB = ∠ACB - ∠ACT = 50° - 20° = 30°

But , ∠TCB = ∠TAB (Angles in the same segment of the circle)

But , ∠TCB or ∠BAT = 30°