∵△BCE∽△AED∴AD/BC=ED/CE∵△ABE∽△CDE∴△AB/CD=AE/ED∵AC是直径∴∠ABC=∠ADC=90º∴tan∠ABD×tan∠ADB＝tan∠ACD×tan∠ACB=(AD/CD)×(AB/BC)=(AD/BC)×(AB/DC)=(ED/CE)×(AE/ED)=AE/EC
