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Question

In the given figure , AC and BC are tangents to the circle with centre O.

If ACB is twice AOB , then ACB = ____


A

150

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B

120

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C

100

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D

60

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Solution

The correct option is B

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 = 2AOB .........(Given)

AOB + 2AOB = 180

3AOB = 180

AOB = 60

AOB = 2×180 = 120


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