HMMT November 2020 U33

In quadrilateral $A B C D$, there exists a point $E$ on segment $A D$ such that $\frac{A E}{E D}=\frac{1}{9}$ and $\angle B E C$ is a right angle. Additionally, the area of triangle $C E D$ is 27 times more than the area of triangle $A E B$. If $\angle E B C=\angle E A B, \angle E C B=\angle E D C$, and $B C=6$, compute the value of $A D^{2}$.