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