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
(a) 80∘
(b) 100∘
(c) 120∘
(d) 140∘
Solution:
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).
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