已知:如圖,點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638605490.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638636323.png)
上,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638636648.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638667391.png)
平分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638683505.png)
,交
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638636323.png)
于點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638776319.png)
.求證:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638792549.png)
為等腰直角三角形.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240216388072850.png)
試題分析:先證
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638823403.png)
為直徑,再通過角的關(guān)系證明
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638839677.png)
即可.
試題解析:由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638854681.png)
,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638823403.png)
為直徑,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638885687.png)
. 2分
由同弧所對(duì)圓周角相等,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638901712.png)
,同理
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638917702.png)
. 4分
又因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638667391.png" style="vertical-align:middle;" />平分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638683505.png)
,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638963708.png)
. 6分
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638839677.png)
,故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638995537.png)
. 8分
從而,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824021638792549.png)
為等腰直角三角形. 10分
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