C2. We consider a triangle $A B C$ and a point $D$ on the extension of $A B$ towards $B$. The point $E$ lies on the side $A C$ such that angle $\angle D B C$ and angle $\angle D E C$ are equal. The intersection of $D E$ and $B C$ is $F$. Suppose that $|B F|=2,|B D|=3,|A E|=4$ and $|A B|=5$. (Note: the image below is not to scale.)

(a) Show that the triangles $\triangle A B C$ and $\triangle A E D$ are similar.

(b) Determine $|C F|$.

![](https://cdn.mathpix.com/cropped/2024_04_17_88f9acd303931df7c94dg-2.jpg?height=485&width=417&top_left_y=2296&top_left_x=1482)