In the given figure , AC and BC are tangents to the circle with centre O.
If ∠ACB is twice ∠AOB , then ∠ACB = ____
120∘
∠OAB = ∠OBC = 90∘ ...........(Tangent is perpendicular to the radius at the point of contact.)
∠AOB + ∠ACB = 180∘ ...........(Sum of angles of a quadrilateral)
But, ∠ACB = 2∠AOB .........(Given)
∠AOB + 2∠AOB = 180∘
3∠AOB = 180∘
∠AOB = 60∘
∴∠AOB = 2×180∘ = 120∘