∫△ABC is an equilateral triangle, ∴ ABC = ∠ ACB = 60, and ∠ OBA = ∠ OBC, ∠ OCA = ∠ OCB,

∴∠OBC=∠OCB=30 .

∵E is perpendicular to OB, ∴ Be = OE, ∴∠ EOB = ∠ OBC = 30, ∴∠ OEF = 60.

∵F is perpendicular to OC, ∴ FC = of, ∴∠ FOC = ∠ OCB = 30, ∴∠ OFE = 60.

∵∠ OEF =∠ OFE = 60, ∴△OEF is an equilateral triangle, ∴ EF = OE = of, and BE = OE, FC = of,

∴BE=EF=FC。