If a chord AB subtends an angle of 60∘ at the centre of a circle,

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  

(a) 30
(b) 60
(c) 90
(d) 120

 

Solution:

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).

 

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