延长BE交AC延长线于F
∵BE⊥AE
∴∠AEB=∠AEF=90°
∵∠BAE=∠FAE AE=AE
∴△AEB ≌△AEF
∴BE=EF
∴BF=2BE
∵∠ACB=90°
∴∠CAD+∠ADC=90°
∵∠CBF+∠BDE=90° ∠ADC=∠BDE
∴∠CAD=∠CBF
∵∠ACD=∠BCF=90° AC=AB
∴△ACD ≌△BCF
∴AD=BF
∴AD=2BE
