gmat preptest, solving for angle DS question

[shadowsjc]

Please see the attachment below. The question stated:

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

1) The degree measure of angle COD is 60 deg
2) The degree measure of angle BCO is 40 deg

Statement 1 is sufficient
Statement 2 is sufficient
Both are sufficient
Each is sufficient alone
1 and 2 are not sufficient

The credited response is D (each statement is sufficient).. but I can't for the life of me figure out why/how. Any thoughts?

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well i stared at it for a bit longer, and I can see how 1 is sufficient (it tells you the length of the small arc CD, and you can calculate BAO from that.

But I still can't understand how 2 is sufficient. I know that giving you BCO will fully define the triangle BCO. But how do you get from there to solving for BAO?

[grockit_jake]

For statement 2,

if BCO = 40, then we know that CBO = 40 since CO = BO in the isosceles triangle.

From the given, we know that

AB = OC (=BO).

If OBC = 40, then ABO = 140, which is the large angle of the isosceles triangle ABO, where AB = BO. Therefore BAO = 40/2 = 20.

Does that make sense?

[shadowsjc]

ah yes that makes sense; it didnt occur to me that both OB and OC were radii (and equal). thanks for the reply

[levocap]

can someone tell me why stmt A is sufficient? still don't see it. thanks