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%%
%% A DANTE-Edition example
%%
%% Example 29-03-1 on page 580.
%%
%% Copyright (C) 2011 Herbert Voss
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%%
%% See http://www.latex-project.org/lppl.txt for details.
%%
%%
%% ====
% Show page(s) 1
%%
\documentclass[]{article}
\pagestyle{empty}
\setlength\textwidth{201.70511pt}
\setlength\parindent{0pt}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\psclip{\pscircle(0,0){4}}
\pstGeonode(1, 2){M}\pstGeonode(-2,2){N}\pstGeonode(0,-2){P}%
\psset{DrawCirABC=false, PointSymbol=none, PointName=none}%
\pstGeonode(0,0){O}\pstGeonode(4,0){A}\pstCircleOA{O}{A}%
\pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{M} sub
\pstDistAB{O}{M} div]{O}{M}[M']%
\pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{P} sub
\pstDistAB{O}{P} div]{O}{P}[P']%
\pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{N} sub
\pstDistAB{O}{N} div]{O}{N}[N']%
\psset{linecolor=green, linewidth=1.5pt}%
\pstCircleABC{M}{N}{M'}{OmegaMN}\pstArcOAB{OmegaMN}{N}{M}%
\pstCircleABC{M}{P}{M'}{OmegaMP}\pstArcOAB{OmegaMP}{M}{P}%
\pstCircleABC{N}{P}{P'}{OmegaNP}\pstArcOAB{OmegaNP}{P}{N}%
\psset{linecolor=blue}
%% la hauteur issue de M
\pstHomO[HomCoef=\pstDistAB{OmegaNP}{N} 2 mul \pstDistAB{OmegaNP}{M} sub
\pstDistAB{OmegaNP}{M} div]{OmegaNP}{M}[MH']
\pstCircleABC{M}{M'}{MH'}{OmegaMH}\pstArcOAB{OmegaMH}{MH'}{M}
%% la hauteur issue de N
\pstHomO[HomCoef=\pstDistAB{OmegaMP}{M} 2 mul \pstDistAB{OmegaMP}{N} sub
\pstDistAB{OmegaMP}{N} div]{OmegaMP}{N}[NH']
\pstCircleABC{N}{N'}{NH'}{OmegaNH}\pstArcOAB{OmegaNH}{N}{NH'}
%% la hauteur issue de P
\pstHomO[HomCoef=\pstDistAB{OmegaMN}{M} 2 mul \pstDistAB{OmegaMN}{P} sub
\pstDistAB{OmegaMN}{P} div]{OmegaMN}{P}[PH']
\pstCircleABC{P}{P'}{PH'}{OmegaPH}\pstArcOAB{OmegaPH}{P}{PH'}
\endpsclip
\end{pspicture}
\end{document}
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