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In the figure above, equilateral hexagon ABCDEF is

Expert replies
by Gmat_mission » Mon Jun 10, 2019 5:08 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty

Image
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
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Source: — Problem Solving |

by Ian Stewart » Mon Jun 10, 2019 6:31 am
"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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Scott@TargetTestPrep » Tue Jun 11, 2019 7:14 pm
Gmat_mission wrote:Image
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

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