AE^2=AO^2+OF^2=(2r)^2+r^2
AE=√[(2r)^2+r^2]
Connect FD, so FD is perpendicular to AE.
Angle Dao = 2 times angle FAD = 60, so angle AEO = 30.
So in Rt triangle DEF,
DE=√3*FD=√3*r