According to the nature of the vertical line, BE=OE and FC=OF.

In the equilateral triangle ABC

∠ABC=∠ACB=60

∫OB and OC are bisectors of∠ b and∠ c respectively.

∴∠OBE=∠BOE=30，∠COF=∠FCO=30

In △OBC, ∠ BOC =180-∠ OBE-∠ FCO =120.

∴∠eof=∠boc-∠boe-= 180-∠OBE-∠cof = 120-60 = 60

Similarly ∠ BeO = ∠ CFO = 120.

Available ∠ OEF = ∠ OFE = 60.

△OEF is an equilateral triangle

∴OE=OF

Then BE=EF=FC