Question 24
Convex quadrilateral $ABCD$ has $AB = 18,$ $\angle A = 60^\circ,$ and $\overline{AB} \parallel \overline{CD}.$ In some order, the lengths of the four sides form an arithmetic progression, and side $AB$ is a side of maximum length. The length of another side is $a.$ What is the sum of all possible values of $a?$