2015 AMC 12B Problem 19

In \triangle ABC, \angle C = 90^\circ and AB = 12. Squares ABXY and CBWZ are constructed outside of the triangle. The points X, Y, Z, and W lie on a circle. What is the perimeter of the triangle?

\textbf{(A)}\; 12+9\sqrt{3} \qquad\textbf{(B)}\; 18+6\sqrt{3} \qquad\textbf{(C)}\; 12+12\sqrt{2} \qquad\textbf{(D)}\; 30 \qquad\textbf{(E)}\; 32

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.