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发表于 2021-6-26 20:25
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本帖最后由 shuxueren 于 2021-6-26 20:51 编辑
【瞭望台】九点圆、九点二次曲线及欧拉线的推广
If AD, BE and CF are 3 cevians concurrent at H, then a conic drawn through any 5 of the 3 feet of the cevians, the 3 midpoints of AH, BH and CH, and the 3 midpoints of the sides of ABC, passes through the remaining 4 points. In addition, the center of the conic N, the centroid G of ABC and H are collinear, and HN = 3GN.
This general result is therefore not only a generalization of the famous nine-point circle, but also of the Euler line.
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