1 . 17世纪法国数学家费马在给朋友的一封信中曾提出一个关于三角形的有趣问题:在三角形所在平面内,求一点,使它到三角形每个顶点的距离之和最小.现已证明:在
中,若三个内角均小于120°,则当点
满足
时,点
到
三个顶点的距离之和最小,点
被人们称为费马点.根据以上知识,已知在
中,
,
,
,
为
内一点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 我国汉代数学家赵爽为了证明勾股定理,创造了一幅“勾股圆方图”,后人称其为“赵爽弦图”,类比赵爽弦图,用3个全等的小三角形拼成了如图所示的等边△
,若
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/5c2057b6-f1c1-472a-abf3-cb041db1b469.png?resizew=174)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/5c2057b6-f1c1-472a-abf3-cb041db1b469.png?resizew=174)
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3卷引用:河南省信阳市百师联盟2022-2023学年高一下学期期中考试数学试题
3 . 我国汉代数学家赵爽为了证明勾股定理,创造了一幅“勾股圆方图”,后人称其为“赵爽弦图”,类比赵爽弦图,用3个全等的小三角形拼成了如图所示的等边
,若
,则AC=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5268cbae6d1747a16bdf3302c597c4a.png)
A.8 | B.7 | C.6 | D.5 |
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4 . 《周髀算经》是我国最早的数学典籍,书中记载:我国早在商代时期,数学家商高就发现了勾股定理,亦称商高定理三国时期数学家赵爽创制了如图1的“勾股圆方图”(以弦为边长得到的正方形
是由4个全等的直角三角形再加上中间的那个小正方形组成),用数形结合法给出了勾股定理的详细证明.现将“勾股圆方图”中的四条股延长相同的长度得到图2.在图2中,若
,
,G,F两点间的距离为
,则“勾股圆方图”中小正方形的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/20f3cfb0-8539-4991-908d-adff543b59a6.png?resizew=373)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/20f3cfb0-8539-4991-908d-adff543b59a6.png?resizew=373)
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解题方法
5 . 我国汉代数学家赵爽为了证明勾股定理,创造了一幅“勾股圆方图”,后人称其为“赵爽弦图”.类比赵爽弦图,用
个全等的小三角形拼成了如图所示的等边
,若
的边长为
,则
的最小值为( )
![](https://img.xkw.com/dksih/QBM/2022/3/22/2941801117802496/2942977848033280/STEM/2aae1abd-06e1-412a-b17d-db0ca946034e.png?resizew=201)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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2022-03-24更新
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4卷引用:河南省中原好教育联盟2021-2022学年高一下学期第二次联考数学试题
河南省中原好教育联盟2021-2022学年高一下学期第二次联考数学试题湖北省部分学校2021-2022学年高一下学期3月联考数学试题(已下线)专题2 赵爽弦图(已下线)第六章 平面向量及其应用(基础、典型、易错、压轴)分类专项训练(2)
6 . 无字证明来源于《几何原本》卷2的几何代数法(以几何方法研究代数问题),通过这一原理,很多的代数的公理或定理都能够通过图形实现证明.现有如图所示
,其中
、
为
边上异于端点的两点,
,
,且
是边长为
的正三角形,则下列不等式一定成立的是( )
![](https://img.xkw.com/dksih/QBM/2021/5/28/2730657997660160/2732120371486720/STEM/621fc4e6-3dce-4375-a13c-06dab1195f8d.png?resizew=244)
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