I had tried Gergely Német's exercise, today, with geogebra. I had already 
done this for a lots of time. The exercise is something like this: show 
that the Feuerbach point is contained by a specific circle. (What's the 
name of the point where the bisector intersects the opposite side? 
Talppont in hungraian. Google translate says that is nadir I don't think 
that) Again: show that Feuerbach point is contained by the circle 
determined by DEF where D E F are the nadirs of bisectors.

I have a lots of part-result (I have 10 hours in it), I was cunstuing the 
excircles and I had seen that the 3 lines, I got when I stand right angle 
lines from excircles centers to the sides,  went throught 1 point. I 
didn't noticed it before. I began thinking about and said: oh, it's an 
trivialism, this is the inogonal conjugate (I heard about it yeasterday