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HMMT 2014 U3

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Let ABCDEFA B C D E F be a regular hexagon. Let PP be the circle inscribed in △BDF\triangle B D F. Find the ratio of the area of circle PP to the area of rectangle ABDEA B D E.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\pi \sqrt{3}}{12}

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