Given a point Q = (u : v : w), for which points P = (x : y : z) are the pedal triangle 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 P and 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 line through the orthocenter of A2B2C2. 3. The locus of the orthology center of A2B2C2 with respect to A1B1C1 is the rectangular hyperbola through P with respect to the triangle A2B2C2.
How about the pedal and antipedal triangles of P (or P and Q, in general)?
ResponderEliminarAnopolitis
Given a point Q = (u : v : w), for which points P = (x : y : z) are the pedal
ResponderEliminartriangle 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 P
and 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 line
through the orthocenter of A2B2C2.
3. The locus of the orthology center of A2B2C2 with respect to A1B1C1 is the
rectangular hyperbola through P with respect to the triangle A2B2C2.