# It is really a Brilliant symbol

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 of $$p+q\sqrt{2}+r\sqrt{3}+s\sqrt{6}$$, where $$p,q,r$$ and $$s$$ are positive integers. Find $$p+q+r+s$$.

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