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DS-Geometry GMATPrep

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DS-Geometry GMATPrep [#permalink] New post 19 Feb 2006, 18:58
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
see attachment
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Geo-Circle-Trig.GIF
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 [#permalink] New post 19 Feb 2006, 20:48
Initially selected B. I solved it again and found it to be D. This is definitely a tough one!

From (1)

See attached picture,

x + (2x+60) +60 = 180
x = 20

From (2)
BCO = CBO = 40 (triangle BCO is isoceles with OB = OC
Angle ABO = 180 - CBO = 140

Also triangle ABO is isoceles with AB = BO
BAO = BOA = x

2x+140 = 180
x = 20

Hence D.
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 [#permalink] New post 19 Feb 2006, 23:01
yup OA is D ...man you are damm good... 8-)

can you please explain why the angle BCO = 2 OAB i.e why x=2x

in this equation
x + (2x+60) +60 = 180
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 [#permalink] New post 19 Feb 2006, 23:06
giddi I got it.. after staring on the figure you have drawn :idea: :idea:
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 [#permalink] New post 19 Feb 2006, 23:19
cool_jonny009 wrote:
yup OA is D ...man you are damm good... 8-)

can you please explain why the angle BCO = 2 OAB i.e why x=2x

in this equation
x + (2x+60) +60 = 180


Because BO = OC = radius
=> Trainge CBO is an isoceles triangle
=>Angle BOC = COB

Now CBO is sum of 2 angles each of which is x. Reason for this is:

There are 2 parallel lines.
1. The diameter
2. The line drawn from B which is parallel to the diameter (say BE)

These two are cut by OB. Angles on the either side of a line (transversal) that cuts two paralle lines are equal. So EBO = BOC

Now CBE = CAO again because diameter is paralle to BE

HTH.

Good luck for your test!! I am sure you will do well.
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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 [#permalink] New post 20 Feb 2006, 18:33
Am almost there but not seeing how you get "x + (2x+60) +60 = 180"

Which line are you calculating the 180 angle for?

Where are you getting 2x+60 from?

Help me please, my brain hurts!!
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 [#permalink] New post 20 Feb 2006, 19:37
Come on guys - GMAT in 2 days - could really do with a bit of help here.

Thanks!
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 [#permalink] New post 20 Feb 2006, 19:43
It doesn't have to be so bad. Angle COD = 60 degrees, therefore angle AOC = 120 degrees.

We're given another angle in triangle AOC, which is BCO, that is, 40 degrees.

For angles in triangle AOC to total 180 degrees, implies:

180 - angle AOC - angle BCO = angle BAO.

180 - 120 - 40 = 20 degrees = angle BAO.

That's it! (assuming ABC is a straight line)
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 [#permalink] New post 20 Feb 2006, 19:52
Ahhhhhhhhhhhhh - Got it. Thanks.

Can go to bed now (is 3.45am in UK and have to work tomorrow)!!!
  [#permalink] 20 Feb 2006, 19:52
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