延长AE交BC的延长线于F
∵BE是∠CBA的角平分线,AE⊥BE
∴△ABF是等腰三角形,E是AF的中点
∵∠BCA = 90°,BE⊥AE,∠BDC = ∠ADE
∴∠CBD = ∠EAD
∵BC = AC
∴△BCD≌△ACF
∴BD = AF
∵AE = AF/2
∴AE = BD/2
∴BD = 2AE