HMMT 2005 U26

In triangle $A B C, A C=3 A B$. Let $A D$ bisect angle $A$ with $D$ lying on $B C$, and let $E$ be the foot of the perpendicular from $C$ to $A D$. Find $[A B D] /[C D E]$. (Here, $[X Y Z]$ denotes the area of triangle $X Y Z$ ).