MathNet 2005 — Part 04 Question 12

In triangle $ABC$, $AC = 3 AB$. Let $AD$ bisect angle $A$ with $D$ lying on $BC$, and let $E$ be the foot of the perpendicular from $C$ to $AD$. Find $[ABD]/[CDE]$. (Here, $[XYZ]$ denotes the area of triangle $XYZ$.)