geometry question

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EddieU: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun May 22, 2011 4:53 amFollowed by: 1 member; Thanked: 1 times

by EddieU » Mon May 30, 2011 1:27 pm

Hi, hopefully someone can help me out with this question:

In the figure attached, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

Thanks in advance.

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: equilateral triangle in circle

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Source: Beat The GMAT — Problem Solving | Mon May 30, 2011 1:27 pm

SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Mon May 30, 2011 1:44 pm

The vertices of an equilateral triangle divide the circumference into 3 equal arcs. Therefore, the arc ABC is 2/3 of the circumference. 24/(2/3) = 36.

This is kind of tricky, because we're used to seeing circumference expressed in terms of pi. If I were going too quickly, and 36 were an option, I wouldn't be surprised if I picked that and moved on. Luckily it's not an answer, so it's easy to realize that you need to divide 36 by pi. pi~3, 36/3 = 12. Since pi is slightly larger than 3, we know the answer must be slightly smaller than 12, so the answer is 11.

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