stonecold 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

\(?\,\,\,:\,\,\,D = 2r\,\,\underline {{\rm{could}}} \,\,{\rm{be}}\)

\(4\pi \,\,\, < \,\,\,{\rm{arc}}\,\,{\rm{length}}\,\,{\rm{ = }}\,\,{1 \over 3}\left( {2\pi r} \right)\,\,\, < \,\,\,6\pi \,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,\,\,{\rm{and}}\,\,\, \cdot \,\,3} \,\,\,\,\,4 \cdot 3\,\,\, < \,\,2r\,\, < \,\,6 \cdot 3\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left( D \right)\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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