Question

In the given figure, O is the centre of the circle AB is a chord and AT is the tangent at A. If ∠AOB = 100^∘ then ∠BAT is equal to [CBSE 2011]
(a) 40^∘
(b) 50^∘
(c) 90^∘
(d) 100^∘

Answer 1

Given: AO and BO are the radius of the circle
Since, AO = BO
∴ △AOB is an isosceles triangle.
Now, in △AOB
∠AOB + ∠OBA + ∠OAB = 180^∘ (Angle sum property of triangle)
⇒ 100^∘ + ∠OAB + ∠OAB = 180^∘ (∠OBA = ∠OAB)
⇒ 2∠OAB = 80^∘
⇒ ∠OAB = 40^∘
We know that the radius and tangent are perperpendular at their point of contact
∵∠OAT = 90^∘
⇒ ∠OAB + ∠BAT = 90^∘
⇒ ∠BAT = 90^∘ − 40^∘ = 50^∘
Hence, the correct answer is option (b).