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Equilateral triangle ABC is inscribed inside a circle. Arc

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Director
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Equilateral triangle ABC is inscribed inside a circle. Arc [#permalink] New post 14 Oct 2006, 11:48
Equilateral triangle ABC is inscribed inside a circle. Arc ABC measures 24; what is the diameter of the circle?

Answer was 11. Would someone kindly explain? Thanks.
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Re: geometry question on Powerprep [#permalink] New post 14 Oct 2006, 12:04
Without any diagram given, this is how I started solving it.

An equilateral triangle inscribed in a circle will create 3 arcs: AB, BC and CA.

Let the center of circle be O. Then angle AOC = angle AOB = angle BOC = 120 degrees (2 x 60)

Thus arc AB=arc BC=arc AC
Therefore ARC ABC = 2/3 x perimeter of circle

24 = 2/3 x Pi x D
D= 36/Pi

But this gives me the diameter as 11.45 and not 11. So, I am not sure where am I going wrong,
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 [#permalink] New post 14 Oct 2006, 12:10
Actually, the problem called for the "approximate" value of the diameter. So you are right. Thanks.
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  [#permalink] 14 Oct 2006, 12:10
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Equilateral triangle ABC is inscribed inside a circle. Arc

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