(1)证明:连接OC······································································· 1分
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230052292946285.jpg)
∵OA=OC
∴∠OAC=∠OCA
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082300522931065.gif)
∵CE是⊙O的切线
∴∠OCE=90° ·············································· 2分
∵AE⊥CE
∴∠AEC=∠OCE=90°
∴OC∥AE ·················································· 3分
∴∠OCA=∠CAD ∴∠CAD=∠BAC
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823005229310453.gif)
∴DC=BC ··························································································· 4分
(2)∵AB是⊙O的直径 ∴∠ACB=90°
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823005229325752.gif)
·························································· 5分
∵∠CAE=∠BAC ∠AEC=∠ACB=90°
∴△ACE∽△AB
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082300522934172.gif)
C······················································································ 6分
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823005229356593.gif)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823005229388454.gif)
······················································ 7分
∵DC=BC=3
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408230052294031013.gif)
····················································· 8分
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823005229419971.gif)
-----------9分 (其它解法参考得分)