Axiome Archimedes

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

\directlua{
   z.O_1     = point:   new  (0, 0)
   z.O_2     = point:   new  (0, 1)
   z.A       = point:   new  (0, 3)
   z.F       = point:   polar (3, math.pi/6)
   L.FO1     = line:    new   (z.F,z.O_1)
   C.O1A     = circle:  new  (z.O_1,z.A)
   z.E       = intersection ( L.FO1 ,C.O1A)
   T.EFO2    = triangle: new ( z.E,z.F,z.O_2)
   z.X       = T.EFO2 : parallelogram ()
   L.XO2     = line: new    (z.X,z.O_2)
   C.O2A     = circle: new  (z.O_2,z.A)
   z.C,z.D   = intersection (L.XO2 , C.O2A)}

\begin{tikzpicture}[ scale = 1.5]
\tikzset{new/.style={color=orange,line width=.2pt}}
\tkzGetNodes 
\tkzDrawCircles(O_1,A O_2,A)
\tkzDrawSegments[new](O_1,A E,F C,D)
\tkzDrawSegments[purple](A,E A,F)
\tkzDrawPoints(A,O_1,O_2,E,F,C,D)
\tkzLabelPoints(A,O_1,O_2,E,F,C,D)
\end{tikzpicture}
\end{document}