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Question
In the given Figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°. Then ∠BOC is equal to ______
Options
40°
50°
140°
150°
Solution
It is known that the tangent is perpendicular to the radius through the point of contact.
∴ ∠ABO = ∠ACO = 90°
Using angle sum property in quadrilateral ABOC:
∠ABO + ∠BOC + ∠ACO + ∠BAC = 360°
⇒ 90° + ∠BOC + 90° + 40° = 360°
⇒ ∠BOC + 220° = 360°
⇒ ∠BOC = 360° - 220° = 140°
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