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Geometry- Circle

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Geometry- Circle [#permalink] New post 08 May 2008, 04:08
Can anyone pls help.
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Re: Geometry- Circle [#permalink] New post 08 May 2008, 06:41
Since O is the center of a semicircle and B,C,D lie on the semicircle:

BO = OC = OD

We know AB = OC (from question stem) so, BO = OC = OD =AB

We know that in a triangle if 2 sides are equal in length, then they have the same angle

In triangle AOB, since AB = OB, angle(BAO) = angle (BOA)
In triangle BOC, since OB = OC, angle(OBC) = angle (OCB)

(1) angle (COD) = 60, Thus, angle (COA) = 180 - 60 = 120.
Not sufficient
(2) angle (BCO) = 40 which means angle (CBO) = 40 [They are equal angles]
So, angle(BOC) = 180-40-40 = 100
Not sufficient

When you combine the 2 statements, angle(COA) = 120 and angle (BOC) = 100
So, angle (BOA) = 20.
We already know angle (BOA) = angle (BAO)

Thus, both (1) and (2) together yield angle (BAO) = 20.

Answer is C.
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Re: Geometry- Circle [#permalink] New post 08 May 2008, 07:05
i get B..

lets see..i know triangle BCO is issoceles..if I know BCO..then i also know CBO.. if know CBO then i know that 180-CBO=ABO..

i know triangle ABO is isso too..so AOB=BAO..

i think B should be the answer..
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Re: Geometry- Circle [#permalink] New post 08 May 2008, 07:53
1. The degree measure of angle COD is 60.

If we are given that COD is 60 degrees, then angle COA must be 120 degrees (180 - 60). This does not help us with angle BAO that we are trying to find.

Insufficient. Thus, eliminate A & D.

2. The degree measure of angle BCO is 40.

We are given BCO, but this measure alone does not help us with finding BAO. Thus eliminate B.

Trying both together, in triangle ACO, in order to find one angle measurement, you would need 2 angles out of 3. Combining both 1 and 2 together, we are given that. By being provided the measurement of angle COD in 1, you can find COA as 120 degrees. Further, in 2 you are given the measure of BCO, which is 40. Combining the two, the result is 160 degrees (120 + 40 = 160). Subtracting 160 from 180 will give you 20 degrees as the measurement for angle CAO, thus providing enough info. to solve the problem.

Eliminate E.

Answer is C.
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Re: Geometry- Circle [#permalink] New post 08 May 2008, 08:00
fresinha12 wrote:
i get B..

lets see..i know triangle BCO is issoceles..if I know BCO..then i also know CBO.. if know CBO then i know that 180-CBO=ABO..

i know triangle ABO is isso too..so AOB=BAO..

i think B should be the answer..


fresinha, you're right. I completely overlooked that we know ABO =140 based on B
and ABO + 2*BAO = 180

Answer should be B
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Re: Geometry- Circle [#permalink] New post 11 Nov 2008, 07:55
Hi guys,

sorry for coming it up again, but it is not well solved.

AO is D

Any idea why?
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Re: Geometry- Circle [#permalink] New post 11 Nov 2008, 09:04
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1. AB=OC=OB ---> triangles ABO and BOC are isosceles.
2. BAO=BOA, OBC=BCO
3. ABO=180-OBC ---> 180-2*BAO=180-BCO ---> BAO=BCO/2 (second condition)
4. COD=180-AOB-BOC=180-BAO-(180-2*BCO)=180-BAO-180+2*2*BAO=3BAO ---> BAO=COD/3 (first condition)
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Re: Geometry- Circle [#permalink] New post 16 Nov 2008, 08:55
Thank you so much Walker

+1 kudos!

Could you explain the way in which you assume that the line CBA is a straight line? That's the only point I miss

This problem is really tough

Thank you


walker wrote:
1. AB=OC=OB ---> triangles ABO and BOC are isosceles.
2. BAO=BOA, OBC=BCO
3. ABO=180-OBC ---> 180-2*BAO=180-BCO ---> BAO=BCO/2 (second condition)
4. COD=180-AOB-BOC=180-BAO-(180-2*BCO)=180-BAO-180+2*2*BAO=3BAO ---> BAO=COD/3 (first condition)

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Re: Geometry- Circle [#permalink] New post 16 Nov 2008, 09:47
Expert's post
JohnLewis1980 wrote:
Could you explain the way in which you assume that the line CBA is a straight line? That's the only point I miss


GMAT gives you the figure and at this figure CBA is a line. It is so unusual maybe even unreal that GMAT uses such geometric illusion :)
At least I've never seen such type of ambiguity in real problems.
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Re: Geometry- Circle [#permalink] New post 17 Nov 2008, 02:22
mmm, ok, I see

thanks again Walker!

walker wrote:
JohnLewis1980 wrote:
Could you explain the way in which you assume that the line CBA is a straight line? That's the only point I miss


GMAT gives you the figure and at this figure CBA is a line. It is so unusual maybe even unreal that GMAT uses such geometric illusion :)
At least I've never seen such type of ambiguity in real problems.

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I'm not linked to GMAT questions anymore, so, if you need something, please PM me

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Re: Geometry- Circle   [#permalink] 17 Nov 2008, 02:22
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