%% 
%%  A DANTE-Edition example
%% 
%% 
%%  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}