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

Question

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. Q.jpg 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. A.jpg

abcgroove · Answer

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.

cyberjadugar · Answer

Hi,

Think about it some more!

Regards,

gmatsaga · Answer

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.

cyberjadugar · Answer

Hi,

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

Regards,

abcgroove · Answer

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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evg88 · Answer

I guess the answer is E. Taking the two statements together we get that the area of the circle is 36*pi "square units".

kashishh · Answer

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

Answer - C

cyberjadugar · Answer

Posted the OA in the question.

Regards,

gmatsaga · Answer

Can you explain why (E) is the answer?

cyberjadugar · Answer

Posted the solution in the question.

Regards,

obs23 · Answer

Good problem, though was confused by the phrase "area of circle passing points"...what is the source of the problem? Thanks!

almogsr · Answer

correct answer should be C, need to change OA.
st1--> if ABC = 60, and AOC = 120 this only tells us the O is the center of the circle. NS
st2--> OA = 6 tells us nothing, point O can be any point inside the circle with no special meaning. NS
st1+2--> if O is the center, than OA is a radius, therefore the area of the circle is is known pi*r^2

correct answer is C

rprashar · Answer

It should be C angle AOC is twice the angle which the arc makes with the point B which is on the circle, this proves that O is the center of this circle 
And when you combine the second statement then you have the radius thus the area

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djmobley · Answer

Statement I is NOT suff - and here's why:

I think the problem here is everyone is assuming what that picture is supposed to look like.

You are all assuming the diameter cuts straight from point B to O and then to the other side of O. Imagine angle ABO starts shrinking - what would happen? Well angle ABC would still be fixed at 60 degrees and point B would start shifting towards the right - right? Well if that is the case then the whole 120 being double 60 so O must be the center argument goes out the door.

never assume these drawings are drawn to the scale they look.

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

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