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°

Answer 1

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°