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GMATPrep - DS Geometry

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allenkt Senior | Next Rank: 100 Posts Default Avatar
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GMATPrep - DS Geometry

Post Wed May 09, 2007 9:03 am
I'm sure there is some property of congruent angles that I don't remember that would help me solve this one but I'll be darned if I know what it is.
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jayhawk2001 Community Manager
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Post Wed May 09, 2007 3:43 pm
Nice question !

OB=OC = radius. So angles BCO and CBO are equal.

Since AB=OC, we have AB=OC=OB. So angles BAO and BOA are equal.

Also, exterior angle CBO = sum of interior angles = BOA + BAO

Let x = BAO. We have

BAO = x = BOA and CBO = BCO = 2x

1 - sufficient. COD = 60 implies COA = 120 = COB + BOA
COB = 180 - 4x (property of triangles)
COB + BOA = 180 - 4x + x = 180 - 3x = 120.
We can solve for x and hence get BAO

2 - sufficient. BCO = 2x. So, we can get x and hence angle BAO.

Hence D.

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