∵BE⊥AC,CF⊥AB,BE=CF,∠A=∠A
∴△ABE≌△ACF(AAS)
∴AB=AC,∠ABE=∠ACF
∵AB=AC
∴∠ABC=∠ACB
∵∠ABE=∠ACF
∴∠DBC=∠DCB
∴BD=CD