证：
连接AE,AD的垂直平分线交BC的延长线于点E
∠BAD=∠CAD
EA=ED
∠EAD=∠EDA
∠EAD=∠EAC+∠CAD
∠EDA=∠BAD+∠DBA=∠CAD+∠DBA(△外角定理)
∴∠EAC=∠DBA=∠EBA
∵∠AEC=∠BEA
∴△AEC∽△BEA
∴EA/EB=EC/EA
EA^2=EC*EB
EA=ED
∴ED^2=EC*EB