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X(1), X(20), X(64), X(1379), X(1380), X(3413), X(3414), X(39641), X(39642)
X(39641), X(39642) are the imaginary foci of the Brocard inellipse, on the Brocard axis and the Kiepert hyperbola, see Table 79
A1, B1, C1 : traces of the trilinear polar of X(3)
A2, B2, C2 : cevians of X(20)
M1, M2 mentioned at Q170 and their isogonal conjugates N1, N2
anti-points, see Table 77
See Q170 for explanations.
A, B, C are double points with tangents passing through X(64) and the corresponding traces of the orthic axis on the sidelines of ABC.
Q171 meets the Kiepert hyperbola at 12 points : A, B, C (each twice), X(3413), X(3414), X(39641), X(39642), N1, N2.
Q171 meets the Darboux cubic K004 at 18 points : A, B, C (each thrice), in/excenters, X(20), X(64), A2, B2, C2.
Q171 meets the McCay cubic K003 at 18 points : A, B, C (each twice), in/excenters, X(39641), X(39642), anti-points.