Bunuel wrote:

If the side of the regular hexagon above is 2, what is the circumference of the inscribed circle?

A. 2∏√3

B. 3∏

C. 4∏/√3

D. 2∏/√3

E. ∏√3

We can break up the hexagon into 6 equilateral triangles in which each side is equal to 2.

If we “cut” one of the equilateral triangles in half, we have a 30-60-90 right triangle. The ratio of the sides of a 30-60-90 triangle are x : x√3 : 2x.

We see that the side opposite the 30-degree angle = 1, and thus, the side opposite the 60-degree angle, which also represents the radius of the circle, is √3. We now can determine the circumference of the circle.

Circumference = 2Πr = 2Π(√3) = 2Π√3

Answer: A

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Jeffery Miller

Head of GMAT Instruction

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