10. Let ABC be a triangle and P a point.
Denote:
Ab, Ac = the orthogonal projections of A on PB,PC, resp.
Na1 = the NPC center of AAbAc
Na2 = the NPC center of Na1AbAc.
Similarly Nb1, Nb2 and Nc1, Nc2.
The lines Na1Na2, Nb1Nb2, Nc1Nc2 are parallel.
11. If P = I,
the lines Na1Na2, Nb1Nb2, Nc1Nc2 are parallel to Euler Line of ABC
21. Let ABC be a triangle.
Denote:
Na1 = the NPC center of IBC
Na2 = the NPC center of Na1BC.
Similarly Nb1,Nb2, Nc1,Nc2
The lines Na1Na2, Nb1Nb2, Nc1Nc2 are parallel to Euler Line of ABC
31. Let ABC be a triangle and IaIbIc the antipedal triangle of I (excentral triangle)
Denote:
Ab, Ac = the orthogonal projections of A on IaIc, IaIb, resp.
Na1 = the NPC center of AAbAc
Na2 = the NPC center of Na1AbAc
The lines Na1Na2, Nb1Nb2, Nc1Nc2 are parallel to Euler Line of ABC
41. Let ABC be a triangle and IaIbIc the antipedal triangle of I (excentral triangle)
Denote:
Na1 = the NPC center of IaBC
Oa = the circumcenter of IaBC
Nao1 = The NPC center of OaBC.
Similarly Nb1, Nbo1, Nc1, Nco1.
The lines Na1Nao1, Nb1Nbo1, Nc1Nco1 are parallel to OI line of ABC.
Antreas P. Hatzipolakis, 1 October 2014
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