Problem of the Week
Problem D
A Triangle and a Rectangle

Point $B$ lies on line segment $AC$, in between $A$ and $C$, so that $BC=10\times AB.$ Line segment $DE$ is parallel to $AC$ so that $BCDE$ forms a rectangle and $ABE$ forms a right-angled triangle.

If $AE=25$ and $BD=74$, determine the exact value of the length of $AD.$