Axiome Archimedes
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\documentclass[landscape,margin=12pt]{standalone}
\usepackage[lua]{tkz-euclide}
\usepackage{tkz-elements}
\begin{document}
\begin{elements}
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: new_polar (3, math.pi/6)
L = line: new (z.F,z.O_1)
C = circle: new (z.O_1,z.A)
z.E = intersection_lc (L,C)
z.x = parallelogram_ (z.F,z.E,z.O_2)
L = line: new (z.x,z.O_2)
C = circle: new (z.O_2,z.A)
z.C,z.D = intersection_lc (L ,C)
\end{elements}
\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}