# 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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