△ABC为等边三角形,所以∠BAC=∠ABC=∠ACB=60
因为∠DAE=120,所以∠DAB+∠EAC=60
∠ABC是△DAB外角,则∠DAB+∠ADB=∠ABC=60
所以∠ADB=∠EAC
∠DBA=∠ACE=120
所以△ABD∽△ECA
BD：AC=AB：CE,BD×CE=AC×AB
因为AB=AC=BC,所以BD×CE=BC²