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.

92°

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°