X(2), X(4), X(64), X(69), X(394), X(2052), X(3346), X(6225), X(6527), X(11413), X(14615)
isogonal conjugates of X(1660), X(1661)
vertices of the antimedial triangle
vertices of the cevian triangle of X(14615)
other points below
Let P be a point with traces X, Y, Z on the sidelines BC, CA, AB of ABC. Denote by Ha the orthocenter of the pedal triangle of X, and define Hb, Hc analogously. The triangle HaHbHc is orthologic to ABC if and only if P lies on K235 (Paul Yiu, Hyacinthos #9868).
K235 is the isotomic pK with pivot P = X(14615) = tg X(20).
K235 meets the circumcircle at the same points as pK(X6, X1370) and the line at infinity at the same points as pK(X6, X394).
K235 is also the locus of M such that the cevian triangle of M is orthologic to the cevian triangle of X(69), the isotomic conjugate of the orthocenter H. See a generalization at Table 7.