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Question

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


  1. 50

  2. 12AOB

  3. 60

  4. 70


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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