Let ABC be a triangle, Aa,Bb,Cc the orth. projections of A,B,C on the Euler line, resp., A1B1C1, A2B2C2 the medial, orthic triangles, resp. and P a point.
Let A'B'C', A"B"C" be the circumcevian triangles of P with respect the triangles A1B1C1, A2B2C2, resp.
Which is the locus of P such that the lines:
1. A'Aa, B'Bb, C'Cc
2. A"Aa, B"Bb, C"Cc
are concurrent?
The Euler line + ??
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Generalization:
P,P* = two isogonal conjugate points.
A1B1C1, A2B2C2 = the pedal triangles of P,P*, resp.
Aa, Bb, Cc = the orth. projections of A,B,C on PP*, resp.
A'B'C', A"B"C" = the circumcevian triangles of a point Q with respect A1B1C1, A2B2C2, resp.
Which is the locus of Q such that the lines:
1. A'Aa, B'Bb, C'Cc
2. A"Aa, B"Bb, C"Cc
are concurrent?
Is it the line PP* + ??
Locus of point of concurrence? Common Circumcircle of A1B1C1 and A2B2C2 + ??
APH, 13 February 2012
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