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Geometry question

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by disco82 » Fri Jun 19, 2009 5:01 am
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.
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Source: — Data Sufficiency |
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by bluementor » Fri Jun 19, 2009 5:54 am
"<" 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-
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by disco82 » Fri Jun 19, 2009 6:06 am
Thanks
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