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Area of circle

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by gmat009 » Tue Oct 07, 2008 9:08 pm
An equilateral triangle that has an area of 9 3^1/2 is inscribed in a circle. What is the area of the circle?
A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2
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by amitansu » Tue Oct 07, 2008 9:12 pm
Refer this link : https://www.beatthegmat.com/equilateral- ... 20144.html

If you can search the forum you will get many of these probs' solution.


Amit
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by mehravikas » Wed Oct 08, 2008 6:56 pm
Answer should be 'D'. Please post the OA.
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by vishubn » Wed Oct 08, 2008 7:45 pm
C is the OA
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by mehravikas » Fri Oct 10, 2008 11:04 pm
Sorry that was a typo....my answer is D.

let the side of the triangle be t
area of the triangle would be - 1/2 * t * (square root 3) / 2 * t = 9 3 ^ 1/2.
the side would also be the diameter of the circle. using this u can find the area of the circle.
vishubn wrote:C is the OA
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by mehravikas » Sun Oct 12, 2008 12:38 am
Hello VishuBn,

Can you please explain how did you get 12 pi....

vishubn wrote:C is the OA
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by parallel_chase » Sun Oct 12, 2008 10:37 am
mehravikas wrote: the side would also be the diameter of the circle. using this u can find the area of the circle.
Side of an equilateral triangle can never be the diameter of the circle. draw a circle with a triangle inscribed in it. Refer to the link listed above by "amitansu". It literally shows you how C is the answer.
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by mehravikas » Sun Oct 12, 2008 11:15 am
I was right upto calculating the height of the triangle. But wasnt aware of this - Finally , R (Circum radius)=2/3 * Height

Is this formula only applicable when the triangle is equilateral??
parallel_chase wrote:
mehravikas wrote: the side would also be the diameter of the circle. using this u can find the area of the circle.
Side of an equilateral triangle can never be the diameter of the circle. draw a circle with a triangle inscribed in it. Refer to the link listed above by "amitansu". It literally shows you how C is the answer.
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by parallel_chase » Sun Oct 12, 2008 11:21 am
mehravikas wrote:I was right upto calculating the height of the triangle. But wasnt aware of this - Finally , R (Circum radius)=2/3 * Height

Is this formula only applicable when the triangle is equilateral??
Well it depends upon the question, but rest assured that it is a standard formula for equilateral triangle.
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