In the figure above, equilateral hexagon ABCDEF is

[Gmat_mission]

In the figure above, equilateral hexagon ABCDEF is inscribed in the circle with center G, which has a diameter of 16. What is the length of AB?

A. \(16\)

B. \(8\sqrt{3}\)

C. \(6\sqrt{3}\)

D. \(8\)

E. \(4\sqrt{3}\)

[spoiler]OA=D[/spoiler]

Source: Princeton Review

[Ian Stewart]

"Equilateral" means "equal sides". It is not a synonym for "regular", which means "equal sides *and* equal angles". Now, it's true that an equilateral hexagon that you can inscribe in a circle must be regular, but the GMAT certainly would never expect a test taker to know that.

So if this were a GMAT question, it would tell you the hexagon is regular, not that it is "equilateral". If we connect the center G of a regular hexagon to each vertex (A, B, C, D, E and F) we divide the hexagon into six equilateral triangles. The edges GA, GB, etc, of each equilateral are each radii of the circle, so they are 8 units long, and since the triangles are equilateral, the edges of the hexagon must also be 8 units long.

[Scott@TargetTestPrep]

In the figure above, equilateral hexagon ABCDEF is inscribed in the circle with center G, which has a diameter of 16. What is the length of AB?

A. \(16\)

B. \(8\sqrt{3}\)

C. \(6\sqrt{3}\)

D. \(8\)

E. \(4\sqrt{3}\)

[spoiler]OA=D[/spoiler]

An equilateral hexagon can be broken up into 6 equal, equilateral triangles. Since the diameter of the circle is 16, each side of the triangle must be 8, and thus side AB (which also makes up a side of one of the equilateral triangles must also be 8.

Anaswer: D

Source: Princeton Review