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