%% 
%%  Ein Beispiel der DANTE-Edition
%%  
%%  7. Auflage
%% 
%%  Beispiel 28-03-1 auf Seite 623.
%% 
%%  Copyright (C) 2016 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[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{193.16928pt}
\setlength\parindent{0pt}
%StartShownPreambleCommands
\usepackage[dvipsnames]{pstricks}
\usepackage{pst-eucl}
%StopShownPreambleCommands
\begin{document}
\begin{pspicture}(-4.5,-1.5)(4.5,4)% Dominique Rodriguez
  \psset{PointSymbol=none}
  \pstTriangle(-4,-1){A}(1,3.5){B}(4,-1){C}
  { \psset{linestyle=none, PointSymbolB=none, PointNameB=none}
    \pstMediatorAB{A}{B}{K}{KP}
    \pstMediatorAB{C}{A}{J}{JP}
    \pstMediatorAB{B}{C}{I}{IP} }
  \pstInterLL[PointSymbol=square,PosAngle=-170]{I}{IP}{J}{JP}{O}
  { \psset{nodesep=-0.8,linecolor=green}
    \pstLineAB{O}{I}\pstLineAB{O}{J}\pstLineAB{O}{K} }
  \psdot[dotstyle=square](O)
  \pstProjection{B}{A}{C}
  \pstProjection{B}{C}{A}
  \pstProjection{A}{C}{B}
  \psset{linecolor=blue}\ncline{A}{A'}\ncline{C}{C'}\ncline{B}{B'}
  \pstInterLL[PointSymbol=square]{A}{A'}{B}{B'}{H}
  % le cercle d'Euler (centre au milieu de [OH])
  \pstMiddleAB[PointSymbol=o, PointName=\omega]{O}{H}{omega}
  \pstCircleOA[linecolor=Orange, linestyle=dashed, dash=5mm 1mm]{omega}{B'}
  \psset{PointName=none}
  % il passe par le milieu des segments joignant l'orthocentre et les sommets
  \pstMiddleAB{H}{A}{AH}\pstMiddleAB{H}{B}{BH}\pstMiddleAB{H}{C}{CH}
  \pstSegmentMark{H}{AH}\pstSegmentMark{AH}{A}
  \psset{SegmentSymbol=wedge}\pstSegmentMark{H}{BH}\pstSegmentMark{BH}{B}
  \psset{SegmentSymbol=cup}\pstSegmentMark{H}{CH}\pstSegmentMark{CH}{C}
\end{pspicture}
\end{document}
