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Question
In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If ∠ACO = 30°,
find: (i) ∠ BCO (ii) ∠ AOB (iii) ∠ APB
Solution
(i) ∠ BCO = ∠ ACO = 30° .....( ∴ C is the intersecting point of tangents AC and BC)
(ii) ∠ OAC = ∠ OBC = 90°
∠ ACO = 30° .....(Given)
∠ AOC = ∠ BOC = 180° - (90° + 30°) ....(Sum of the angles of a Δ is 180°)
∠ AOC = 180° - 120°
∠ AOC = 60°
∠ AOB = ∠ AOC + ∠ BOC
∠ AOB = 60° + 60° = 120°
(iii) ∠ APB = `1/2"∠ AOB" = (120°)/2 = 60°` .....( ∴ Angle substended at the remaining part of the circle is half the ∠ substended at the centre)
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