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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