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X(1), X(3), X(2574), X(2575)

excenters

details and other points below

Let P be a point and let H', H" be the orthocenters of the pedal and anticevian triangles of P respectively. P, H', H" are collinear if and only if P lies on the circular septic Q196. See the comparable octic Q018.

Points on Q196

• A, B, C which are double with tangents passing through X(3) and the traces of the trilinear polar of X(3) on the sidelines of ABC.

• the in/excenters X(1), Ia, Ib, Ic with tangents also passing through X(3).

• X(3) with tangent passing through X(64).

• vertices A', B', C' of the incentral triangle i.e. cevian triangle of X(1)

• traces A" B", C" of the antiorthic axis i.e. trilinear polar of X(1).

• vertices A1, B1, C1 of the 2nd circumperp triangle i.e. circumcevian triangle of X(1).

• their reflections A2, B2, C2 in X(3), vertices of the 1st circumperp triangle.

• midpoints A3, B3,C3 of AA', BB', CC', on the internal bisectors and on the sidelines of the medial triangle.

• midpoints A4, B4,C4 of AA", BB", CC", on the external bisectors and on the sidelines of the medial triangle.

• infinite points of the sidelines of ABC. The asymptotes pass through the corresponding midpoints of OA, OB, OC.

• circular points at infinity with isotropic tangents concurring at X(2070).

• infinite points X(2574), X(2575) of the Jerabek hyperbola with tangents concurring at X on the lines {X5, X539}, {X22, X156}, {X110, X1154}, {X155, X2929}, etc, SEARCH = 1.24880615141169. X is now X(71742) in ETC.