An equilateral triangle is inscribed in a circle

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

An equilateral triangle is inscribed in a circle

by VJesus12 » 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 4Ï€ and 6Ï€, 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.

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Source: Beat The GMAT — Problem Solving | Thu Mar 01, 2018 6:10 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » 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 4Ï€ and 6Ï€, 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 4Ï€ = 12Ï€ and 3 x 6Ï€ = 18Ï€. Therefore, the diameter of the circle will be between 12Ï€/Ï€ = 12 and 18Ï€/Ï€ = 18. So 15 could be the value of the D.

Answer: D

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