Denote:
Ab = (Parallel to BC through A*) /\ AC
Ac = (Parallel to BC through A*) /\ AB
Bc = (Parallel to CA through B*) /\ BA
Ba = (Parallel to CA through B*) /\ BC
Ca = (Parallel to AB through C*) /\ CB
Cb = (Parallel to AB through C*) /\ CA
1. Oa, Ob, Oc = the circumcenters of A'AbAc, B'BcBa, C'CaCb, resp.
The triangles ABC, OaObOc are orthologic
The locus of the orthologic center (OaObOc, ABC), as t varies, is the Euler line of ABC.
Which is the locus of the other orthologic center (ABC, OaObOc)?
2. Na, Nb, Nc = the NPCs centers of A'AbAc, B'BcBa, C'CaCb, resp.
The triangles ABC, NaNbNc are orthologic
The locus of the orthologic center (NaNbNc, ABC), as t varies, is the Euler line of ABC.
Which is the locus of the other orthologic center (ABC, NaNbNc)?
Antreas P. Hatzipolakis, 6 April 2013
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