Olympiad Geometry · Challenge problem

Triangle $ABC$ has $AB = 9$, $AC = 12$ and $BC = 15$. Point $D$ lies on $\overline{AB}$ with $AD = 4$, and point $E$ lies on $\overline{AC}$ so that $\triangle ADE \sim \triangle ACB$ (with $A \to A$, $D \to C$, $E \to B$). Find $DE$.