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}
\begin{tkzelements}
scale = 1.5
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)
\end{tkzelements}
\begin{tikzpicture}
\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}