A, B, C are three points on a circle. The tangents at A meets extended line BC at T. ∠BTA = 42°, ∠CAT = 46°. The angle subtended by BC at the centre of circle is.
Answer & explanation
Correct answer: option 3
In ΔACT,
∠ATC + ∠CAT + ∠ACT = 180°
42° + 46° + ∠ACT = 180°
∠ACT = 180° - 88°
∠ACT = 92°
O is center of circle.
∠OAC = 90° - 46° = 44°
∠OAC = ∠OCA = 44° [ OA = OC = Radius]
Now, ∠BCO + ∠OCA + ∠ACT = 180°
∠BCO + 44° + 92° = 180°
∠BCO = 44°
Now, ∠BCO = ∠CBO = 44°
In ΔBOC,
∠BOC + ∠BCO + ∠CBO = 180°
∠BOC = 180° - 88° = 92°