2005 AMC 10B Problem 23

In trapezoid ABCD we have \overline{AB} parallel to \overline{DC}, E as the midpoint of \overline{BC}, and F as the midpoint of \overline{DA}. The area of ABEF is twice the area of FECD. What is AB/DC?

\mathrm{(A)} 2 \qquad \mathrm{(B)} 3 \qquad \mathrm{(C)} 5 \qquad \mathrm{(D)} 6 \qquad \mathrm{(E)} 8

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