求解四点共圆一题

hbghlyj

关于Laguerre定理、圆环点, 见此帖

isee

hbghlyj 发表于 2022-3-24 05:03
前面
@予一人
大佬说的挺好的了，但这里也说一下从三角形几何学角度的做法，顺便补充一下垂心在外接等轴 ...

应该指出是原作者，或者转载，否则粗一看以为是原创

hbghlyj

hbghlyj 发表于 2022-3-23 21:59
https://www.zhihu.com/question/55992071/answer/1326118715
抄一下(作为备份
这个结果事实上是圆锥曲线的 ...

原文链接在18#

isee

hbghlyj 发表于 2022-11-7 22:44
原文链接在18#

原来有哇~~~

hbghlyj

几何画板官网
Advanced Sketch Gallery(高级作图画廊) #Beyond Euclid
Minkowskian Geometry闵考夫斯基几何的工具箱
Through the Looking Glass A glimpse of Euclid’s twin geometry The Minkowski geometry
Through the Looking Glass A glimpse of Euclid’s twin geometry The Minkowski geometry.pdf (514.59 KB, Downloads: 8)

2022-11-8 01:25 Upload

Click on the file to download the attachment

The nine-point configuration
a) The nine-point circle: [有一个图在上述PDF中, 这里就不上传了.]
b) The nine-point hyperbola: [有一个图在上述PDF中, 这里就不上传了.]
Notice that both cases are special cases of a theorem in affine geometry, which says that the heights in the triangle can be replaced by any set of three lines from the vertices passing through the same point. This gives rise to nine points through which a unique conic passes, the nine-point conic.
• In the case of an ellipse, you may consider the configuration to be a parallel projection of the nine-point circle.
• In the case of a hyperbola, you may similarly consider the configuration to be a parallel projection of the nine-point hyperbola.