1 . 著名数学家欧拉提出了如下定理:三角形的外心、重心、垂心依次位于同一直线上,且重心到外心的距离是重心到垂心距离的一半.此直线被称为三角形的欧拉线,该定理被称为欧拉线定理.现已知
的三个顶点坐标分别为
,
,
,圆
的圆心
在
的欧拉线上,且满足
,直线
被圆
截得的弦长为
.
(1)求
的欧拉线的方程;
(2)求圆
的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8796f6d3e7a0e3771f83df47e99a970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473cb51e930729ed70b6c60ac011906f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5558ffa6dc28d437c0467c7f361d444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4071fb64529cf85e8e418d2faab628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94fcf57347aec685a8fca271aba14eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2022-10-11更新
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