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An equilateral triangle is inscribed in a circle of...

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by BTGmoderatorLU » Tue Nov 28, 2017 5:59 pm
An equilateral triangle is inscribed on 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 D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by ErikaPrepScholar » Wed Nov 29, 2017 10:02 am
An equilateral triangle inscribed in a circle will create three arcs of equal length. If each arc is between 4Ï€ and 6Ï€, then the circumference of the circle can be between 3(4Ï€) and 3(6Ï€) - or between 12Ï€ and 18Ï€.

Circumference of a circle is π * diameter, so the diameter of the circle can be between 12 and 18. The only answer between 12 and 18 is D, 15.
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