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- Feb 14, 2012

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A regular 12-gon is inscribed in a circle of radius 12. The sum of the lengths of all sides and diagonals of the 12-gon can be written in the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}$, where $a,\,b,\,c$ and $d$ are positive integers. Find $a+b+c+d$.

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