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# In the below figure, O is the centre of the circle. What is

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In the below figure, O is the centre of the circle. What is [#permalink]  13 Feb 2006, 15:41
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In the below figure, O is the centre of the circle. What is angle ABC?

1. OAC = 45 Degrees
2. AOC = 100 Degrees
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Circle.jpg [ 7.12 KiB | Viewed 587 times ]

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I think it is B.

Angle AOC = 100
Angle AOC (outer) = 260

Angle ABC = 1/2*(Outer) Angle AOC = 130.
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TeHCM wrote:
giddi77 wrote:
I think it is B.

Angle AOC = 100
Angle AOC (outer) = 260

Angle ABC = 1/2*(Outer) Angle AOC = 130.

Giddi,

How did you get 260?

See the attached picture.

On a chord (inside the same arc), angle subtended at the center is 2 times angle subtended at the circumference.

(outer) Angle AOC = 360 -100 = 260
Hence Angle ABC = 260/2 = 130.

Aslo I did Google search and found this:
http://www.saltire.com/applets/chordang/chordang.htm

You can infact drag the point B and see how the angle changes... that will make it very clear
Attachments

Circle.doc [25 KiB]

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if B is sufficient shouldnt A be sufficient too since u can get the value of AOC if you know the values of OAC?
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Quote:
On a chord (inside the same arc), angle subtended at the center is 2 times angle subtended at the circumference.

(outer) Angle AOC = 360 -100 = 260
Hence Angle ABC = 260/2 = 130.

Yeah I understand this logic....I guess I was a little confused by your work.

If AOC is 100, then arc ABC would be 200.

Then the rest of the arc would be 360-200 = 160 ==> angle ABC would be 80

Yes, if we know OAC, then we'd know AOC, so the answer should be D
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ps_dahiya wrote:
giddi77 wrote:
I think it is B.

Angle AOC = 100
Angle AOC (outer) = 260

Angle ABC = 1/2*(Outer) Angle AOC = 130.

Bingo !!!! OA is B.

I don't get it. how can OA be B? Why isn't A sufficient?
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It puzzles me too, why 1stm is not suf. If we know angle OAC we know that angle AOC=180-2angleOAC. From that we can find ABC.

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Natalya Khimich wrote:
It puzzles me too, why 1stm is not suf. If we know angle OAC we know that angle AOC=180-2angleOAC. From that we can find ABC.

Agree. with TeHCM, trublu, Natalya.
Didn't think carefully It should be D!

Also. I think this is not an ETS question. I have seen for ETS questions, if the answer is D. Both solutions give *exactly* the same answer.

Here:

From (1) AOC = 180-45*2 = 90 which is not the same as (2) where AOC =100

ps_dahiya what is the source of the question?
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What figure? How do I see the figure?
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Now that I see the figure, here is the explaination.

(i)
OAC = OCA = 45 => AOC is 90.
OB is the Bisector of AOC => AOB = 45.
Triangle AOB is Isoceles => OBA = (180-45)/2
Again, OB is the Angle Bisector of ABC, Hence ABC = 180-45 = 135

(A) is sufficient, rule out B,C,E.

(ii)
Same logic as (i)
AOB = 100/2 = 50
OBA = (180-100)/2
ABC = 180-100 = 80

(ii) is sufficient as well. Answer is D
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ps_dahiya wrote:
giddi77 wrote:
I think it is B.

Angle AOC = 100
Angle AOC (outer) = 260

Angle ABC = 1/2*(Outer) Angle AOC = 130.

Bingo !!!! OA is B.

My bad. I just checked the OA again and its certainly D.

I got a document from one of my friends containong around 100-120 DS and 100-120 PS questions. This question is from that document.
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the answer is B...can't be E by any means....
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Sorry to drag an old thread back to life. But I wanted to share one little tip just in case somebody didn't know.

In GMAT DS questions, generally the answers from both conditions (if exist) will be the same. For example, in this question, the GMAT test would have
1. OAC = 40 Degrees
2. AOC = 100 Degrees

OAC is 40 instead of 45 because otherwise you'll get different answers from 1 and 2. This fact may come in handy sometimes when you want to check if you are answering correctly.
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HongHu wrote:
Sorry to drag an old thread back to life. But I wanted to share one little tip just in case somebody didn't know.

In GMAT DS questions, generally the answers from both conditions (if exist) will be the same. For example, in this question, the GMAT test would have
1. OAC = 40 Degrees
2. AOC = 100 Degrees

OAC is 40 instead of 45 because otherwise you'll get different answers from 1 and 2. This fact may come in handy sometimes when you want to check if you are answering correctly.

this is exactly what i was thinking. the question is little flawed.
two statements should not result in different answers cuz real gmat doesnot deal with such an ambigious question.
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