Get: △ CEO △ CGO (SAS),

∴∠EOC=∠GOC,EO=GO，

According to the theorem of triangle interior angle sum, in △ABC,

2∠EBC+2∠FCB+60 = 180，

The solution is ∠ EBC+∠ FCB = 60,

At △DBC, ∠ BDC =180-(∠ EBC+∠ FCB) =180-60 =120.

∴∠FDE=∠BDC= 120，

∵∠BOG+∠GOC= 120，

∵∠ BOG+2∠ GOC = 180，

Solution: ∠ BOG = ∠ GOC = ∠ EOC = 60.

In △BFO and △BGO, ∠FBO=∠GBO, ∠ FOB = ∠ GOB = 60, BO=BO,

∴△BFO≌△BGO，

∴FO=OG，

∴FO=EO.