A geometry problem involving triangles In the figure, AE is the bisector of the exterior angle CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find the length of CE.

My Attempt: I tried to find out the existence of congruent triangles in the diagram, but couldn't find any.
Any help will be appreciated.

Alternatively: Continue the line $D$ until $F$ and connect $F$ with $E$ so that $AC=AD$.
Note that $\Delta ACE$ is equal to $\Delta ADE$, because two sides and the angle between them are equal. It implies the line $AE$ is a bisector in $\Delta BDE$.
Using the property of bisector:
$$\frac{AB}{BE}=\frac{AD}{DE} \Rightarrow \frac{10}{12+CE}=\frac{6}{CE} \Rightarrow CE=18.$$
