2005 AMC 10A Problem 25

In \triangle ABC we have AB = 25, BC = 39, and AC = 42. Points D and E are on \overline{AB} and \overline{AC} respectively, with AD = 19 and AE = 14. What is the ratio of the area of triangle ADE to the area of the quadrilateral BCED?

\textbf{(A) } \frac{266}{1521}\qquad \textbf{(B) } \frac{19}{75}\qquad \textbf{(C) } \frac{1}{3}\qquad \textbf{(D) } \frac{19}{56}\qquad \textbf{(E) } 1

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