（本题满分9分）如图所示，△ABC内接于⊙O，AB是⊙O的直径，点D在⊙O
上，过点C的切线交AD的延长线于点E，且AE⊥CE，连接CD．
（1）求证：DC=BC；
（2）若AB=5，AC=4，求tan∠DCE的值．
（本题满分9分）如图所示，△ABC内接于⊙O，AB是⊙O的直径，点D在⊙O
上，过点C的切线交AD的延长线于点E，且AE⊥CE，连接CD．
（1）求证：DC=BC；
（2）若AB=5，AC=4，求tan∠DCE的值．
（1）证明：连接OC················································································· 1分
∵OA＝OC
∴∠OAC＝∠OCA
∵CE是⊙O的切线
∴∠OCE＝90° ·············································· 2分
∵AE⊥CE
∴∠AEC＝∠OCE＝90°
∴OC∥AE ·················································· 3分
∴∠OCA＝∠CAD ∴∠CAD＝∠BAC
∴
∴DC＝BC ··························································································· 4分
（2）∵AB是⊙O的直径 ∴∠ACB＝90°
∴·························································· 5分
∵∠CAE＝∠BAC ∠AEC＝∠ACB＝90°
∴△ACE∽△ABC······················································································ 6分
∴ ∴
······················································ 7分
∵DC＝BC＝3
∴····················································· 8分
∴-----------9分 (其它解法参考得分)
解析:略