X(4), X(125), X(523), X(1312), X(1313), X(2574), X(2575)
X(2574), X(2575) : infinite points of the Jerabek hyperbola
Ha, Hb, Hc : vertices of the orthic triangle
Ta, Tb, Tc : vertices of the anticevian triangle of X(523)
T1, T2 intersections of the orthic axis and the Kiepert hyperbola
S1, S2 Hirst-incerses of T1, T2 on the tangent at H to the Jerabek hyperbola
K238 is a pK invariant in the Hirst transform with pole X(125) - the center of the Jerabek hyperbola - and conic the Jerabek hyperbola : for any point M on K238, the line MX(125) meets the polar line of M in the Jerabek hyperbola at M' on the cubic. Hence, K238 is a member of the class CL032 of cubics.
K238 has three real asymptotes. One is the perpendicular at H to the Euler line. The remaining two are parallel to those of the Jerabek hyperbola and meet at X(974), the midpoint of X(125)X(185).
The tangents at A, B, C, H pass through X(125). Those at Ha, Hb, Hc, X(125) are perpendicular to the Euler line.
K238 meets the nine point circle at Ha, Hb, Hc, X(115), X(1312), X(1313).
The Hirst inverses of Ha, Hb, Hc are the vertices of the anticevian triangle of X(523).