∵BF⊥AC CE⊥AB
∴∠BED=∠AED=∠CFD=∠AFD
∵∠EDB=∠CDF ∠BED=∠CFD BE=CF
∴△BED≌△CFD
∴DE=DF
∵DE=DF AD=AD ∠AED=∠AFD
∴△AED≌△AFD
∴∠BAD=∠CAD
∴AD平分角BAC
∵BF⊥AC CE⊥AB
∴∠BED=∠AED=∠CFD=∠AFD
∵∠EDB=∠CDF ∠BED=∠CFD BE=CF
∴△BED≌△CFD
∴DE=DF
∵DE=DF AD=AD ∠AED=∠AFD
∴△AED≌△AFD
∴∠BAD=∠CAD
∴AD平分角BAC