四个三角形的欧拉线共点的充要条件是A1A2A3A4四点共圆，或者对角线互相垂直。

hbghlyj · 2024-3-12 03:03

Last edited by hbghlyj 2025-3-21 21:16已知四边形A1A2A3A4对角线分割为四个三角形，要探索这四个三角形的欧拉线何时共点？
四个三角形的欧拉线共点的充要条件是A1A2A3A4四点共圆，或者对角线互相垂直。
如何证明呢

hbghlyj · 2024-12-14 06:11

A. P. Hatzipolakis, F. van Lamoen, B. Wolk, P. Yiu, Concurrency of Four Euler Lines, Forum Geometricorum, Volume 1 (2001) 59-68.

It is known that the locus of P for which the Euler lines (L₂) of triangles PBC, AP C and ABP are concurrent is the union of the circumcircle and the Neuberg cubic.⁸ See [10, p.200].

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[几何] 四个三角形的欧拉线共点的充要条件是A1A2A3A4四点共圆，或者对角线互相垂直。

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