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# i know this one has been discussed before..why is statement

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Current Student
Joined: 28 Dec 2004
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i know this one has been discussed before..why is statement [#permalink]

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19 Jul 2008, 16:38
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

i know this one has been discussed before..why is statement 1 sufficient?
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Senior Manager
Joined: 07 Jan 2008
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19 Jul 2008, 17:02
You know that BO=OC=AB => angle OCB = angle OBC = ~

Also AB=OB => angle BOA = angle BAO = \$ [YOu are asked theta]

1) extend line BO so that you can form exterior angle:
2~ = exterior angle
2~ = \$ + 60 ----I

Now look at triangle ABO:
2\$ + 180-~ = 180
~ = 2\$----II
solve I and II
\$ = 20
A is good.

2) ~=40
Look at triangle ABO:
2\$ + 180-40 = 180
\$ = 20
B is good.

D.

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Senior Manager
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19 Jul 2008, 17:17
IMO D.

You know that BO = OC = AB
Hence Triangles ABO AND OBC are isosceles
This means angles OBC = BCO and BAO = BOA

S2. says BCO = 40 degrees
Hence OBC = 40 degrees and two interior angles of a triange are equal to the sum of the interior angles
This means BAO+BOA = 40 and since they are equal BAO - 20 degrees

S2. COD = 60
Let angle BAO = x
Hence CAO + ACO = 60 degrees (sum of interior angles = exterior angles)
BOC = 180 - (60-x) - (60-x) = 60+2x
BOA = 180 -(60-2x) - 60 = 60-2x

x = 60-2x
x = 20

IMO D

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Intern
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20 Jul 2008, 15:51
I still don't get how S1 is SUFF can someone post a diagram?

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Re: gprep geometry   [#permalink] 20 Jul 2008, 15:51
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# i know this one has been discussed before..why is statement

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