Apollonius circle
[PDF] [TEX]
% !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}