2002 AMC 10A Problem 23

Points A,B,C and D lie on a line, in that order, with AB = CD and BC = 12. Point E is not on the line, and BE = CE = 10. The perimeter of \triangle AED is twice the perimeter of \triangle BEC. Find AB.

\text{(A)}\ 15/2 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 17/2 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 19/2

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