13 Sep
2011
13 Sep
'11
6:29 p.m.
Fred Lunnon: ... let S be the fourth point within the original triangle T, the Cevian lines through S partitioning T into six subsidiary triangles. It looks to me as if not only (1) When S is the incentre of T, then the incentres of the six sub-triangles lie on a conic; but also (2) When S is the centroid of T, then the centroids of the six sub-triangles lie on a conic. ---------- The proposition (2) is invariant under affine transformations. There exists an affine transformation that takes T into an equilateral triangle, in which case, the six centroids lie on a circle. -- Gene