REFLECTING THE CIRCLES (N,NA), (N,NB), (N,NC) ON THE ALTITUDES

Let ABC be a triangle and HaHbHc the orthic triangle.

Denote:

(Na) = the reflection of the circle (N,NA) in AHa

(Nb) = the reflection of the circle (N,NB) in BHb

(Nc) = the reflection of the circle (N,NC) in CHc

1. The circles (Na),(Nb),(Nc) are concurrent at a point P

2. The triangles HaHbHc, NaNbNc are perspective at a point Q.

Antreas P. Hatzipolakis, 22 Febr. 2013