# 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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