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Angle ABC of an equilateral triangle is 60 degrees or 1/3 of the total degrees in a triangle (all of the angles in a traingle add up to 180). Therfore you know the length of arc AC is 1/3 the total circumfrence of the circle, making the other part of the circle, ARC ABC = 2/3 the circumference of the circle. The distance of arc ABC = 24. From there you can set up an equation to solve if you need to:
2/3(Circumference) = 24 Circumference = 36
The formula to find the circumference is (pie)D = Circumference. Substitue in 36 and divide by pie. This should give you just about 11.
I guess most people here are gmatPERPs because of their obsession with the gmat, and most try to get their hands on the newest and most fresh official gmat questions.
i know the triangle is equilateral..so if the perimeter of this is 24..then each side must be 8..
ok..now you really have to look at the diagram...cus thats important..i could arrange a equilateral triangle inside a circle where all sides can be equal to the radius..
anyway..looking at the figure..i see that one lenght is 8..now if i were to draw an isso triangle along the radius with the longer side being 8..i know that isso triangles have sides in the following proportion x:x:sqrt(2)x..
i know the longer side sqrt(2)x=8..lets find x or better yet 2x..since we are looking for diameter..
x=16/sqrt(2) =11.3
11 it is..
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