证明：∵AB•BF=DB•BC，∴AB：BC=DB：BF．∵∠B为公共角，∴△BAC∽△BDF．∴∠A=∠D．∵∠AEF=∠CED，∴△AEF∽△DEC．∴AE：EF=DE：CE．∴AE•CE=DE•EF．
