∵A、B、E、C共圆,∴∠ABC＝∠AEC.
∵AE是直径,∴∠ACE＝90°.
∵AD是△ABC的高,∴∠ADB＝90°.
由∠ABC＝∠AEC、∠ADB＝∠ACE＝90°,得：△ADB∽△ACE,∴AB/AE＝AD/AC,
∴AD×AE＝AB×AC＝√6×√3＝3√2.