## diameter of the circle? (GMAT Prep 2)

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### diameter of the circle? (GMAT Prep 2)

by alex.gellatly » Sat Jul 21, 2012 1:12 am
In the figure below, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

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by shovan85 » Sat Jul 21, 2012 1:38 am
Equilateral Triangle, AB = BC = CA, So, for the circle Arc AB = Arc BC = Arc CA

Arc ABC = Arc AB + Arc BC = 24. Thus, Arc Arc AB = 12 = Arc BC = Arc CA
So, perimeter of the circle = Arc AB + Arc BC + Arc CA = 3* 12 = 36 (as all Arc are same)

=> radius = 36/(2*pie) = 5.73 approx

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by [email protected] » Sat Jul 21, 2012 2:31 am
alex.gellatly wrote:In the figure below, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?
As triangle ABC is equilateral, arc ABC is 2/3 of the circumference of the circle.
Hence, circumference of the circle = 24*3/2 = 36

Hence, diameter of the circle = 36/Ï€ = Slightly less than 36/3 â‰ˆ 11

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by theCEO » Sat Jul 21, 2012 2:49 am
shovan85 wrote:Equilateral Triangle, AB = BC = CA, So, for the circle Arc AB = Arc BC = Arc CA

Arc ABC = Arc AB + Arc BC = 24. Thus, Arc Arc AB = 12 = Arc BC = Arc CA
So, perimeter of the circle = Arc AB + Arc BC + Arc CA = 3* 12 = 36 (as all Arc are same)

=> radius = 36/(2*pie) = 5.73 approx

IMO 5
Right solution. However question asked for diameter.

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by Lifetron » Sat Jul 21, 2012 7:20 am
All the arcs are equal.
So, 2*3.14*r=36. We need 2r.
2r=36/3.14=11(approx)