过点F作FM⊥AC于M,过点G作GN⊥BC于N
∵CE平分∠ACB
∴∠ACE＝∠BCE
∵AD⊥BC,FM⊥AC,CF＝CF
∴△CDF全等于△CMF
∴DF＝MF
∵GN⊥BC,AD⊥BC,FG∥BC
∴矩形FGND
∴DF＝GN
∵AD⊥BC
∴∠CAD+∠ACB＝90
∵∠BAC＝90
∴∠B+∠ACB＝90
∴∠B＝∠CAD
∴△AFM全等于△BGN
∴BG＝AF
∵∠DCF+∠CFD＝90,∠ACF+∠AEC＝90,∠ACE＝∠BCF
∴∠CFD＝∠AEC
∵∠CFD＝∠AFE
∴∠AEC＝∠AFE
∴AE＝AF
∴BG＝AE
∵AE＝2,AB＝7
∴EG＝AB-AE-BG＝7-2-2＝3