IMC 1999 — Keystage 3 (IWYMIC) — individual Question 14

In the diagram below, $BC\perp AC$. A point $D$ on $BC$ satisfies $BC=4BD$, and a point $E$ on $AC$ satisfies $AC=8CE$. If $AD=164$ cm and $BE=52$ cm, determine the length, in cm, of $AB$.