% !TEX TS-program = lualatex
% Created by Alain Matthes on 2023.
\documentclass{standalone} 
\usepackage[mini]{tkz-euclide}
\usepackage{tkz-elements}
\begin{document}
\directlua{dofile("apob-lua.lua")}
   
\begin{tikzpicture}[scale =.25]
\tkzGetNodes
\tkzFillCircles[green!30](O,xa)
\tkzFillCircles[teal!30](Ja,Ea Jb,Eb Jc,Ec)
\tkzFillCircles[lightgray](S,a)
\tkzFillCircles[green!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}
 

init_elements()
z.A = point(0, 0)
z.B = point(6, 0)
z.C = point(0.8, 4)
T.ABC = triangle(z.A, z.B, z.C)
z.N = T.ABC.eulercenter
z.Ea, z.Eb, z.Ec = T.ABC:feuerbach():get()
z.Ja, z.Jb, z.Jc = T.ABC:excentral():get()
z.S = T.ABC:spieker_center()
C.JaEa = circle(z.Ja, z.Ea)
C.ortho = C.JaEa:orthogonal_from(z.S)
z.a = C.ortho.south
C.euler = T.ABC:euler_circle()
z.O = C.ortho:inversion(C.euler).center
z.xa, z.xb, z.xc = C.ortho:set_inversion(z.Ea, z.Eb, z.Ec)