Question 21
In the diagram, $ABCD$ is a convex quadrilateral. Its diagonal $AC$ meets $BD$ at the midpoint $E$ of $BD$. The perpendicular from $A$ to $DE$ has foot $H$, in the interior of segment $DE$. Given $\angle BCA=90^\circ$, $CE=12\text{ cm}$, $EH=15\text{ cm}$, $AH=40\text{ cm}$ and $CD=x\text{ cm}$, find $x$.
