REFLECTIONS OF AI,BI,CI IN A LINE THROUGH I

Let ABC be a triangle, L a line through I and La,Lb,Lc the reflections of AI, BI, CI in L.

Denote:

Ab,Ac = the orthogonal projections of A on Lb,Lc, resp.

Bc,Ba = the orthogonal projections of B on Lc,La, resp.

Ca,Cb = the orthogonal projections of C on La,Lb, resp.

The Euler lines of AAbAc, BBcBa, CCaCb are concurrent on a point Q on the pedal circle of I (= incircle of ABC)

Antreas P. Hatzipolakis, 4 Febr. 2013