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

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i know this one has been discussed before..why is statement [#permalink]  19 Jul 2008, 15:38
i know this one has been discussed before..why is statement 1 sufficient?
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Re: gprep geometry [#permalink]  19 Jul 2008, 16:02
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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Re: gprep geometry [#permalink]  19 Jul 2008, 16:17
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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Re: gprep geometry [#permalink]  20 Jul 2008, 14:51
I still don't get how S1 is SUFF can someone post a diagram?
Re: gprep geometry   [#permalink] 20 Jul 2008, 14:51
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