AMC 12B 2012 Problem 21

Square A X Y Z is inscribed in equiangular hexagon A B C D E F with X on \overline{B C}, Y on \overline{D E}, and Z on \overline{E F}. Suppose that A B=40 and E F=41(\sqrt{3}-1). What is the side-length of the square?

Answer Choices
A. 29 \sqrt{3}
B. \dfrac{21}{2} \sqrt{2}+\dfrac{41}{2} \sqrt{3}
C. 20 \sqrt{3}+16
D. 20 \sqrt{2}+13 \sqrt{3}
E. 21 \sqrt{6}