ABCD is a convex quadrilateral with AC and BDintersecting 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?

ABCD is a convex quadrilateral with AC and BDintersecting 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?