Find length of a line in similar triangles

Question

I have a triangle same as in this image:

I want to find the length of $DE$ while $AC$, $AB$, $CB$, $CD$ are known.

Up to now I have tried to calculate it as follows:

$$L = \frac{AC\ (AB - CD)}{AB}$$

I am not sure whether this is right or not.

Answer 1

$$\begin{align} \frac{AC}{AB}&=\frac{DE}{BE}\\ (CB-CD)^2+DE^2&=BE^2\\ \end{align} $$ Solve this system for $BE$ and $DE$