题目内容
(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.
长线于点C,作,垂足为D,若,,求DE的长.
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
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
略
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