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

A, B, C (triple)

Ia, Ib, Ic : excenters

Ha, Hb, Hc : feet of altitudes

Ka, Kb, Kc : feet of the Lemoine axis (centers of the apollonian circles)

X(2574), X(2575) : points at infinity of the Jerabek hyperbola

vertices of the circumnormal triangle (on the McCay cubic)

Let P be a point and let H', H" be the orthocenters of the pedal and antipedal triangles of P respectively. P, H', H" are collinear if and only if P lies on the octic Q018 or on the line at infinity.

Q018 has five singular points : A, B, C (triple) and the circular points at infinity (double). The tangents at A are the line AO and two other perpendicular lines passing through the intercepts of the circle centered at Oa = AO /\ BC through A and BC.

Q018 has two real asymptotes which are parallel to those of the Jerabek hyperbola. It meets the circumcircle at the vertices of the circumnormal triangle.

When "antipedal" is replaced by "anticevian", we obtain the circular septic Q196.