%!TEX TS-program = lualatex
%Created by Alain Matthes on 2023-11-10
%Copyright (c) 2023 AlterMundus.
\documentclass[margin=10pt]{standalone}
\usepackage[mini]{tkz-euclide}
\usepackage{tkz-elements}
\begin{document}

\directlua{dofile("southpole.lua")}

\begin{tikzpicture}[scale=1.5]
   \tkzGetNodes
   \tkzDrawCircles(W,A I,Ha)
   \tkzDrawArc(S,C)(B)
   \tkzDrawPolygon(A,B,C)
   \tkzDrawSegments[orange](A,S B,S C,S)
   \tkzDrawLine(B,I)
   \tkzDrawPoints(A,B,C,I,I_A,W,S,Ha)
   \tkzFillAngles[green!30,opacity=.3](A,S,B A,C,B)
   \tkzFillAngles[red!30,opacity=.3](B,C,S B,A,S)
   \tkzFillAngles[blue!30,opacity=.3](S,B,C S,A,C)
   \tkzLabelPoints(I,W,S)
   \tkzLabelPoints[above](A)
   \tkzLabelPoints[below right](I_A,C)
   \tkzLabelPoints[below left](Ha,B)
\end{tikzpicture}

\end{document}

init_elements()
z.A = point(2, 4)
z.B = point(0, 0)
z.C = point(8, 0)
T.ABC = triangle(z.A, z.B, z.C)
z.I, z.Ha = T.ABC:in_circle():get()
z.W = T.ABC.circumcenter
C.WA = circle(z.W, z.A)
z.S = C.WA.south
z.I_A = intersection(line(z.A, z.S), line(z.B, z.C))