Pedal Triangles of Isogonal Conjugates

Abstract

Let ABC be a triangle and P be a point. The reflections of the three lines AP, BP, and CP in the angle bisectors at A, B, and C meet in a point I, called the isogonal conjugate of P. The feet of the perpendiculars from P to the sides of triangle ABC form the pedal triangle of P, RST. Similarly, let the pedal triangle of I be UVW. Then R, S, T, U, V, W all lie on a circle.