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Regular 12-gon

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March 21, 2006
trigonometryAMCAIMEtrig identitiesLaw of Cosines

Problem Statement

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+b2+c3+d6, a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6}, where aa, bb, cc, and dd are positive integers. Find a+b+c+da + b + c + d.
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