How about the pedal and antipedal triangles of P (or P and Q, in general)?Anopolitis
Given a point Q = (u : v : w), for which points P = (x : y : z) are the pedaltriangle of P and the pedal triangle of Q orthologic?We have the following results:1. The locus of points P = (x : y : z) such that the pedal triangle A1B1C1 of Pand the pedal triangle A2B2C2 of Q are orthologic is the line OQ.2. The locus of the orthology center of A1B1C1 with respect to A2B2C2 is a linethrough the orthocenter of A2B2C2.3. The locus of the orthology center of A2B2C2 with respect to A1B1C1 is therectangular hyperbola through P with respect to the triangle A2B2C2.