# AIME problem

Geometry Level 5

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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