联结AF∵EF平分AD∴AF=DF易知∠BAD+∠ABF=∠ADF=∠DAF=∠DAC+∠CAF∵∠BAD=∠DAC∴∠ABF=∠CAF又∠AFB=∠AFC∴△AFB∽△CFA∴AF*AF=BF*CF∵AF=DF∴FD*FD=FB*FC