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Question

In the figure, if OAB=40, ACB is equal to


A

50

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B

12AOB

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C

60

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D

70

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Solution

The correct options are
A

50


B

12AOB


In ΔOAB,
OA=OB [radii]
OAB=OBA=40 [angles opposite to equal sides are equal]
Also,
AOB+40+40=180 [angle sum property of a triangle]
AOB+40+40=180
AOB=18080=100
We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
AOB=2ACB
100=2ACB
ACB=1002=50


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