I had tried Gergely N√©met'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
from professor Hrask√) of the center of incircle.
But I didn't come closer to the solution of the original exercise.