1 . 如图,分别以
的两边
为边向外作正三角形
及
,设
交于
用复数证明:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83515d91f26944fa2ad00fcbe76a6a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6c03b3e996be358f19f7014fef026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c503e29373e8d87134bdb46bd3912910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcfdccb24c195e2be43b6c89214feef.png)
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2020-01-31更新
|
743次组卷
|
6卷引用:人教B版(2019) 必修第四册 逆袭之路 第十章 复数 本章小结
人教B版(2019) 必修第四册 逆袭之路 第十章 复数 本章小结(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)第十章 复数 本章小结(已下线)7.3复数的三角表示C卷人教B版(2019)必修第四册课本习题第十章本章小结(已下线)第七章 复数(基础、典型、易错、压轴)分类专项训练(2)
2 . 在正
的平面内有任一点
(不在
的三条高线所在直线上),点
关于直线
、
、
的对称点为
,
、
.证明:
的外心在一条直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5614fbac899088deaed1298a62e2ff5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5614fbac899088deaed1298a62e2ff5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f445af60a2950f1bf61ab76c8682451c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d48101bb735f309819728150e20d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9076974ebd6331d67055302be8167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b8e635cc02acb2cb541429157cd28.png)
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3 . 已知
为任意凸四边形.分别以
、
为边在四边形外作正
和正
,以
、
为底边在四边形外作顶角为
的等腰三角形
和
.求证:
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34a9667453c05bc78de93ba5313e734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b0c3bc854308c01e4a8bb5e0995620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84288b493b64c3a30466fb9075621da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa485cf3776f36aaf4abaadaf30fb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01f6f70b5cb3fd3b580e9f298588d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfa17ce4597d93782a605b929c55e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf491301d68ddc4951dd5a321c2c91f7.png)
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4 . 已知圆内接六边形ABCDEF的末尾两位数字是的边满足关系式AB=CD=EF=r,r为圆的半径,G、H、K分别是边BC、DE、FA的中点.试说明△GHK是否为正三角形.
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