题目内容
来 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
,
, 则DE的长为 .![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408230133076413400.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307609555.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307609628.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307625443.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408230133076413400.png)
3
∵BC切⊙O于B,∴∠ABC=90°,
∵∠ACB=60°,∴∠BAC=30°,∴AC=2BC=8,
由勾股定理得:AB=
=
∴OA=
AB=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307703436.png)
∵OD⊥AE,∴∠ADO=90°,∴OD=
OA=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307719346.png)
在△ADO中,由勾股定理得:AD=3,∵OD⊥AE,OD过圆心O,∴AD=DE=3,
∵∠ACB=60°,∴∠BAC=30°,∴AC=2BC=8,
由勾股定理得:AB=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307656670.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307672424.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307687343.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307703436.png)
∵OD⊥AE,∴∠ADO=90°,∴OD=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307687343.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823013307719346.png)
在△ADO中,由勾股定理得:AD=3,∵OD⊥AE,OD过圆心O,∴AD=DE=3,
![](http://thumb.zyjl.cn/images/loading.gif)
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