如圖,四邊形ABCD是半徑為1的圓O的外切正方形,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857747553.png)
是圓O的內(nèi)接正三角形,當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857747553.png)
繞著圓心O旋轉(zhuǎn)時(shí),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857778563.png)
的取值范圍是( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/2014082404185779310182.png)
試題分析:以O(shè)為原點(diǎn)建系,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418578713680.jpg)
則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857887501.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857903498.png)
,設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857918738.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418579341176.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041857949949.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418579651279.png)
,
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418579812223.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418579961075.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418580121039.png)
,
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041858027946.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240418580431090.png)
.
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