CAT 2025 Geometry & Mensuration — Previous Year Question

In $\triangle A B C , A B = A C = 12 \mathrm {~cm}$ and $D$ is a point on side $B C$ such that $A D = 8 \mathrm {~cm}$. If $A D$ is extended to a point $E$ such that $\angle A C B = \angle A E B$, then the length, in cm , of $A E$ is