Maximising an Angle!

In $\triangle ABC$ , $\angle ABC = 90^{\circ}$ and $AB = 50$ meters. $D$ is a point on $AB$ such that $AD=40$ meters. What is the length of $BC$ so that $\angle ACD$ is maximized. If the length of $BC$ can be written as $a\sqrt{b}$ , where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime, find $a+b$ in meters.