Assuming I am interpreting your problem correctly, I get half what you got for the length of a side:
This means we can let ED=x and then
CD=10 and AB=20. Therefore, OC=OD=5 and OA=OB=10.
Then, the radius of the circle is OE.
Solving for x we see
Check my figures. Perhaps too much New Year's cheer.
If I misinterpreted the diagonal lengths, adjust accordingly.