Distance to Diagonal Intersection

Geometry Level 4

\(ABCD\) is a convex quadrilateral with \(AC\) and \(BD\) intersecting at \(E\). \(F\) is a point on \(AD\) such that \(EF\) is parallel to \(CD\). It is given that the circumcircle of triangle \(AED\) is tangential to \(DC\). If \(FD= 336\) and \(FA = 420\), what is \(ED\)?

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