Geometry question

[disco82]

It's a long question, so I've included it in the file attached. I know the correct answer but haven't been able to figure out why it is so. The correct answer is D.

[bluementor]

"<" denotes angle.

CO is the radius of the semi-circle. Since BO is also the radius, we have;

AB = CO = BO

This means triangles ABO and COB are isosceles triangles, with:

<BAO = <BOA = x

and

<OBC = <OCB

From this we can evaluate <ABO = 180 - 2x

So, <OBC = 180 - <ABO = 2x, and therefore, <COB = 180 - 4x


what is x?

statement 1: <COD = 60

<COD + <COB + <BOA = 180
60 + x + 180 - 4x = 180
3x = 60
x = 20

Sufficient.

Statement 2: <BCO = 40

<BCO = <CBO = 2x = 40,

x = 20

Sufficient.

Choose D.

-BM-

[disco82]

Thanks