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High school mathematics-geometry proof selection.
Solution: Make DG‖AB in G through point D.

D is the midpoint of BC DG‖BE.

∴DG is the center line of △ △CBE.

∴DG=? exist

∫AE:EB = 1:2

∴AE=? exist

∴AE=DG

∫DG‖AB

∴∠AEF=∠DGF,∠EAF=∠GDF

∠AEF=∠DGF,AE=DG∠EAF=∠GDF

∴△AEF≌△DGF

∴AF=FD

(Then you can prove that the area of triangle FDC is equal to half of triangle ADC, and the area of triangle ADC is equal to half of triangle ABC, so the area of triangle FDC is equal to a quarter of triangle ABC), that is, 4∶ 1.