MathDB

12

Part of 1990 AIME Problems

Problems(1)

Regular 12-gon

Source:

3/21/2006
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.
trigonometryAMCAIMEtrig identitiesLaw of Cosines