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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.

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

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25 Jun 2012, 20:53

cyberjadugar 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.
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt

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

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25 Jun 2012, 21:16

gmatsaga wrote:

cyberjadugar 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.

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

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27 Jun 2012, 01:17

cyberjadugar wrote:

Posted the OA in the question.

Regards,

Can you explain why (E) is the answer?
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat. - T. Roosevelt

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