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# What is the area of circle passing points A, B & C (in the

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What is the area of circle passing points A, B & C (in the [#permalink]

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25 Jun 2012, 08:39
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What is the area of circle passing points A, B & C (in the given figure), if the angle ABC is 60?

(1) Angle AOC is 120.
(2) OA is 6 units.
Attachment:
File comment: Rough Diagram

Q.jpg [ 18.97 KiB | Viewed 1791 times ]

[Reveal] Spoiler: Solution
As per the below diagram, lets say a circle is passing through AOC.
angle AOC = angle AEC, so, irrespective of the fact that O is center or not, it is possible to have any angle as twice of angle ABC.

Thus, even after combining the two statement we can't figure out whether O is center of the circle.

Remember, the angle subtended by arc at the center is twice of the angle subtended by the arc on rest of the circumference but the converse is not true.
Attachment:

A.jpg [ 15.11 KiB | Viewed 1559 times ]
[Reveal] Spoiler: OA

Last edited by cyberjadugar on 27 Jun 2012, 03:09, edited 2 times in total.
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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25 Jun 2012, 09:36
Both statements are required.
We need the first to prove that 'O' is the centre of the circle and second one to know the radius.
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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25 Jun 2012, 18:16
ankushgrover wrote:
Both statements are required.
We need the first to prove that 'O' is the centre of the circle and second one to know the radius.

Hi,

Regards,
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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25 Jun 2012, 19:53
What is the area of circle passing points A, B & C (in the given figure), if the angle ABC is 60?

(1) Angle AOC is 120.
(2) OA is 6 units.

I was supposed to answer B. But that is wrong, why? Because the sufficiency of answer B is pivoted on the assumption that O is indeed the center of the circle. But, this is not the case. The question doesn't tell us that O is the center of the circle. This is a very good assumption/data sufficiency question. It doesn't necessarily mean that ABC is 60 that AOC is already 120. That'd be a wrong assumption. What is OA is an arc? or OA is a line segment not connected to the center?

Now, as like what the poster said above, we need A to prove that O is the center. Now that we know O is the center and from (2) we know that OA is 6 units, we know that the radius of the circle is 6. From that we can know the area of the circle.
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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25 Jun 2012, 20:16
gmatsaga wrote:
What is the area of circle passing points A, B & C (in the given figure), if the angle ABC is 60?

(1) Angle AOC is 120.
(2) OA is 6 units.

I was supposed to answer B. But that is wrong, why? Because the sufficiency of answer B is pivoted on the assumption that O is indeed the center of the circle. But, this is not the case. The question doesn't tell us that O is the center of the circle. This is a very good assumption/data sufficiency question. It doesn't necessarily mean that ABC is 60 that AOC is already 120. That'd be a wrong assumption. What is OA is an arc? or OA is a line segment not connected to the center?

Now, as like what the poster said above, we need A to prove that O is the center. Now that we know O is the center and from (2) we know that OA is 6 units, we know that the radius of the circle is 6. From that we can know the area of the circle.

Hi,

Again, a little more thinking required...and I would say it's safe to assume OA is line segment.

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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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26 Jun 2012, 02:30
I would say i've thought enough and i will still go with my original answer!!

Plz provide the correct answer and explanation..

Thanks

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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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26 Jun 2012, 02:36
I guess the answer is E. Taking the two statements together we get that the area of the circle is 36*pi "square units".
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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26 Jun 2012, 14:53
given information -
1.) A, B, C are on circle
2.) angle ABC = 60
area of circle = ?

St. 1) Angle AOC = 120, when Angle ABC = 60
Angle AOC is central angle BUT Not sufficient

St. 2.) OA= 6 - Not sufficient

1 + 2
OA is the radius hence area of circle = 36pi - Sufficient

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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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26 Jun 2012, 18:52
Posted the OA in the question.

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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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27 Jun 2012, 00:17
Posted the OA in the question.

Regards,

Can you explain why (E) is the answer?
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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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27 Jun 2012, 03:11
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Posted the solution in the question.

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Re: What is the area of circle passing points A, B & C (in the [#permalink]

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17 Sep 2013, 07:21
Posted the solution in the question.

Regards,

Good problem, though was confused by the phrase "area of circle passing points"...what is the source of the problem? Thanks!
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Re: What is the area of circle passing points A, B & C (in the   [#permalink] 17 Sep 2013, 07:21
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