Radius of semi circle is r say. OC=OB=OD=r. Therefore AB=r.

Statement 1 just gives the value of COB. All I can get is COA = 120 and CAO + ACO = 120. We need CAO (BAO). So, this is not enough.

Statement 2:
i) BCO = 40. This implies CBO is also 40 (OC = OB and isosceles triangle).
ii) from i, ABO = 140 (180-40). and BAO + BOA = 40.
iii) AB = OB (Given)
Hence BAO is equal to BOA. Hence BAO = 20.

Therefore statement2 itself is sufficient.

What is the OA?

is OA d ?

1 ]

AB = OB = OC

now COD = 60

AOB + BOC + COD = 180

triangle BOC is isosceles triangle ... let's angle OBC = BCO = x
hence BOC = 180 - 2x

therefore our eqn becomes AOB + 180 - 2x + COD = 180

now ABO + OBC = 180
ABO + x = 180


even ABO is isosceles triangle .. let's say AOB = BAO = y

2y + ABO = 180
therefore 2y + 180 - x = 180
hence y = x / 2

putting y = x/2 in our previous equation

x/2 + 180 - 2x + 60 = 180

hence x = 40

therefore y = 20 ...i.e BAO = 20

2 ] already replied by jay2007

I fell into the same trap and went with B...OA is D

I agree with your reasoning..but from the information in (1) we know that angle A and angle C have to sum 60 degrees. They don't in your answer....

y = 20 and x = 40

edited