2010 AMC 10A Problem 14

Triangle ABC has AB=2 \cdot AC. Let D and E be on \overline{AB} and \overline{BC}, respectively, such that \angle BAE = \angle ACD. Let F be the intersection of segments AE and CD, and suppose that \triangle CFE is equilateral. What is \angle ACB?

\textbf{(A)}\ 60^\circ \qquad \textbf{(B)}\ 75^\circ \qquad \textbf{(C)}\ 90^\circ \qquad \textbf{(D)}\ 105^\circ \qquad \textbf{(E)}\ 120^\circ

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