% !TEX TS-program = lualatex
% Created by Alain Matthes on 2024-12-25.
% Copyright (c) 2024 AlterMundus.
\documentclass[margin = 12pt]{standalone}
\usepackage[mini]{tkz-euclide}
\usepackage{tkz-elements}
\begin{document}

\directlua{dofile("lua/" .. tex.jobname .. ".lua")}

\begin{tikzpicture}[  scale = .6]
	\tkzGetNodes
	\tkzFillCircles[purple!30](O,xa)
	\tkzFillCircles[teal!30](Ja,Ea Jb,Eb Jc,Ec)
	\tkzFillCircles[cyan!20](S,a)
	\tkzFillCircles[purple!30](N,Ea)
	\tkzDrawPoints(xa,xb,xc)
	\tkzClipCircle(O,xa)
	\tkzDrawLines[add=3 and 3](A,B A,C B,C)
	\tkzDrawCircles(Ja,Ea Jb,Eb Jc,Ec S,a O,xa N,Ea)
	\tkzDrawPoints(O,A,B,C,S,Ea,Eb,Ec,N)
	\tkzDrawSegments[dashed](S,xa S,xb S,xc)
	\tkzLabelPoints(O,N,A,B)
	\tkzLabelPoints[right](S,C)
\end{tikzpicture}

\end{document}

% The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles