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## An equilateral triangle is inscribed in a circle

tagged by: VJesus12

This topic has 1 expert reply and 0 member replies

### Top Member

VJesus12 Master | Next Rank: 500 Posts
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#### An equilateral triangle is inscribed in a circle

Thu Mar 01, 2018 6:10 am
An equilateral triangle is inscribed in a circle of diameter D. If the length of the arc bounded by the adjacent corners of the triangle is between 4π and 6π, then which of the following could be the value of D?

A)6.5
B)9
C)11.9
D)15
E)23.5

The OA is the option D.

Experts, can you show me an image that can help me? I am confused. Could you show me the way to solve this PS question? Thanks in advanced.

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
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Fri Mar 02, 2018 10:04 am
VJesus12 wrote:
An equilateral triangle is inscribed in a circle of diameter D. If the length of the arc bounded by the adjacent corners of the triangle is between 4π and 6π, then which of the following could be the value of D?

A)6.5
B)9
C)11.9
D)15
E)23.5
Since there are 3 arcs bounded by the adjacent corners of an equilateral triangle, and since the lengths of these 3 arcs are equal, the circumference of the circle will be between 3 x 4π = 12π and 3 x 6π = 18π. Therefore, the diameter of the circle will be between 12π/π = 12 and 18π/π = 18. So 15 could be the value of the D.

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Scott Woodbury-Stewart Founder and CEO

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