Question

In the given figure, AB and AC are tangents to a circle with centre O such that ∠BAC = 40^∘ .Then ∠BOC is equal to [CBSE 2011, 14]
(a) 80^∘
(b) 100^∘
(c) 120^∘
(d) 140^∘

Answer 1

We know that the radius and tangent are perperpendular at their point of contact
∵∠OBA = ∠OCA = 90^∘
Now, In quadrilateral ABOC
∠BAC + ∠OCA + ∠OBA + ∠BOC = 360^∘ [Angle sum property of a quadrilateral]
⇒ 40^∘ + 90^∘ + 90^∘ + ∠BOC = 360^∘
⇒ 220^∘ + ∠BOC = 360^∘
⇒ ∠BOC = 140^∘
Hence, the correct answer is option (d).