CIRCUMCIRCLE

Let ABC be a triangle and P, Q two isogonal conjugate points and P1P2P3, Q1Q2Q3 the pedal triangles of P,Q, resp.

Denote:

R1 = the radical axis of the circles ((P1, P1Q)[=circle centered at P1 with radius P1Q],(Q1, Q1P))

R2 = the radical axis of the circles ((P2, P2Q),(Q2, Q2P))

R3 = the radical axis of the circles ((P3, P3Q),(Q3, Q3P))

The triangles ABC, Triangle A'B'C' bounded by (R1,R2,R3) are perspective at a point D on the circumcircle.

Antreas P. Hatzipolakis, Hyacinthos #21733