# Trisection is cool

Geometry Level 3

$$ABC$$ is a triangle such that $$AC>AB$$, $$D$$ and $$E$$ are points on side $$BC$$ such that $$BD=DC$$ and $$AE$$ perpendicular to $$BC$$. It is known that $$AE$$ and $$AD$$ trisect the angle $$A$$ and $$BC=10\sqrt {3}$$. Find $$AC$$.

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