Assuming I am interpreting your problem correctly, I get half what you got for the length of a side:

Because,

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.

And,

Solving for x we see

Check my figures. Perhaps too much New Year's cheer.

If I misinterpreted the diagonal lengths, adjust accordingly.