Question

If a chord AB subtends an angle of 60^∘ at the centre of a circle, then the angle between the tangents to the circle drawn from A and B isl to [CBSE 2013C]
(a) 30^∘
(b) 60^∘
(c) 90^∘
(d) 120^∘

Answer 1

We know that the radius and tangent are perperpendular at their point of contact
∵∠OBC = ∠OAC = 90^∘
Now, In quadrilateral ABOC
∠ACB + ∠OAC + ∠OBC + ∠AOB = 360^∘ [Angle sum property of a quadrilateral]
⇒ ∠ACB + 90^∘ + 90^∘ + 60^∘ = 360^∘
⇒ ∠ACB + 240^∘ = 360^∘
⇒ ∠ACB = 120^∘
Hence, the correct answer is option (d).