证明:
过点P作BC的平行线MN,交AB于点M,交AC于点N。
所以:PM/BD = AP/AD = PN/DC
因为:D是BD中点,BD = DC
所以:PM = PN,点P是MN的中点
因为:EP/EC = PM/BC = PN/BC = FP/FB
所以:EP/CP = EP/(EC-EP) = FP/(FB-FP) = FP/BP
在△PFE和△PBC中:
∠FPE = ∠BPC
EP/CP = FP/BP
所以:△PFE ∽ △PBC ,
可得:∠PFE = ∠PBC
所以:EF//BC
所以:△AEF∽△ACB
所以:AF/AB=AE/AC