（本题满分8分）如图，AB是⊙O的直径，过B点作⊙O的切线，交弦AE的延长线于点C，作，垂足为D，若，，求DE的长．

题型：不详难度：来源：

（本题满分8分）如图，AB是⊙O的直径，过B点作⊙O的切线，交弦AE的延
长线于点C，作，垂足为D，若，，求DE的长．

答案

解法一：∵BC是⊙O的切线，     ∴．
在Rt△ABC中，∵，∴．
∴．··············································································· 3分
在Rt△AOD中，，∴．···· 6分
∵，   ∴．··························································· 8分
解法二：连接BE．∵AB为直径，∴．
∴．∴．·········································· 3分
在Rt△ABC中，∵，
∴． ∴．························································ 6分
∵，         ∴．·················································· 8分

解析

略