1990 AIME Problems/Problem 12

Problem

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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1990 AIME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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