Apollonius circle

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% !TEX TS-program = lualatex
% Author Alain Matthes 2023
\documentclass[margin=12pt]{standalone} 
\usepackage[mini]{tkz-euclide}
\usepackage{tkz-elements}
\begin{document} 

\directlua{
      z.A                  = point: new (0,0)
      z.B                  = point: new (6,0)
      z.C                  = point: new (0.8,4)
      T.ABC                = triangle : new (z.A,z.B,z.C) 
      C.euler              = T.ABC: euler_circle ()
      z.N,z.Ma             = get_points (C.euler)      
      z.I_a,z.I_b,z.I_c    = get_points (T.ABC : excentral())
      z.Ea,z.Eb,z.Ec       = get_points (T.ABC : feuerbach ())
      % The Feuerbach triangle is the triangle formed by the three points 
      % of tangency of the nine-point circle with the excircles
      z.S,z.p              = get_points (T.ABC: spieker_circle ())
      % z.Xa,z.Xb,z.Xc    = get_points (T.ABC : extouch())
      C.exa                = T.ABC : ex_circle ()
      z.Ia,z.Xa            = get_points (C.exa)
      C.exb                = T.ABC : ex_circle (1)
      z.Ib,z.Xb            = get_points (C.exb)
      C.exc                = T.ABC : ex_circle (2)
      z.Ic,z.Xc            = get_points (C.exc)     
      % S spieker point is the radical center of the last three circles
      L.fa                 = line : new (z.S,z.Ea) 
      L.fb                 = line : new (z.S,z.Eb)
      L.fc                 = line : new (z.S,z.Ec)
      z.f_a                = intersection (L.fa,C.exa)
      z.f_b                = intersection (L.fb,C.exb)
      _,z.f_c              = intersection (L.fc,C.exc)
      T                    = triangle : new ( z.f_a, z.f_b , z.f_c )
      z.o                  = T.circumcenter
      _,z.l                = get_points (C.exa : orthogonal_from (z.S))
      % S center of inversion !!
}

\begin{tikzpicture}[scale = .75]
\tkzSetUpLine[ultra thin,color=teal]
\tkzGetNodes
\tkzDrawCircles[red](o,f_a  N,Ma)
\tkzDrawPoints[red](f_a,f_b,f_c,Ea,Eb,Ec,o,N)
\tkzClipCircle(o,f_a)
\tkzDrawLines[add=3 and 3](A,B A,C B,C)
\tkzDrawCircles(I_a,Xa I_b,Xb I_c,Xc)
\tkzDrawCircles[cyan](S,l)
\tkzDrawPoints(A,B,C)
\tkzDrawPoints[cyan](S)
\tkzDrawSegments[dashed,red](S,f_a S,f_b S,f_c)
\tkzDrawSegments[dashed,teal](o,f_a o,f_b o,f_c)
\end{tikzpicture}
\end{document}