Maximising an Angle!

Level pending

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.

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