SEAMO 2027 - Paper F - SET 07 - Self-study Question 3

$ABCD$ is a convex quadrilateral whose diagonals $AC$ and $BD$ intersect at $E$. Point $H$ lies on segment $DE$ and $AH\perp DE$. Given $BE=ED$, $CE=9$, $EH=12$, $AH=32$ and $\angle BCA=90^\circ$, find $CD$.

Original source figure (schematic), preserving its mathematical labels and arrangement.