Question 12
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 $$
a+b\sqrt2+c\sqrt3+d\sqrt6,
$$ where $a,$ $b,$ $c,$ and $d$ are positive integers. Find $a+b+c+d.$
a+b\sqrt2+c\sqrt3+d\sqrt6,
$$ where $a,$ $b,$ $c,$ and $d$ are positive integers. Find $a+b+c+d.$