B And C Are Three Points On Circle

A, B and C are three points on a circle. The tangent at C meets BN produced at T. Given … the angle subtended by AB at the centre…

Answers:

Join BC. Let O be the centre of the circle. Join OA and OB.

In  △BCT, △ACT,

∠BTC = ∠ATC = 36˚

∠ACT = ∠ABC = 48˚

∠BAC = ∠ACT + ∠ATC

= 48˚ + 36˚ = 84˚

∴    ∠BCA = 180˚ – (∠ABC + ∠BAC)

 = 180˚ – (48˚ + 84˚) = 48˚

∴    ∠BOA  = 2∠BCA

= 2 × 48˚

= 96˚