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