% Urem de Bruxelles - Hugues Vermeiren
\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
	Construction de l'orthocentre d'un triangle

	\bigskip
	\begin{tikzpicture}
		\coordinate[label=above:$A$] (A) at (0,3);
		\coordinate[label=left:$B$] (B) at (-2,0);
		\coordinate[label=right:$C$] (C) at (2,-1);
		%
		\coordinate (D) at ($(A)+(C)-(B)$);	
		\coordinate (E) at ($(B)+(A)-(C)$);	
		\coordinate (F) at ($(C)+(B)-(A)$);
		\draw[orange,thick] (A)--(B)--(C)--cycle;
		%
		\coordinate (HA) at ($(A)!1.5!-90:(D)$);
		\coordinate (HB) at ($(B)!1!-90:(E)$);
		\coordinate (HC) at ($(C)!1!-90:(F)$);
		\coordinate (H) at (intersection of HA--A and HB--B);
		\coordinate (A') at (intersection of HA--A and B--C);
		\coordinate (B') at (intersection of HB--B and C--A);
		\coordinate (C') at (intersection of HC--C and A--B);
		\draw (A)--(A') (A)--(H);% on surécrit pour couvrir tous les cas
		\draw (B)--(B') (B)--(H);
		\draw (C)--(C') (C)--(H);
		\draw[orange,dashed] (A)--(B') (B)--(A') (A)--(C');
		%
		\foreach \i in {A',B',C'}
			\fill (\i) circle (0.6mm);
		\foreach \i in {A,B,C}
			\fill[red,draw=black] (\i) circle (0.8mm);
		\fill[blue!30,draw=black] (H) circle (0.8mm) node[right=0.2cm,black]{$H$};
		%
		\draw[help lines] (D) node{D}--(E) node {E}--(F) node{F}--cycle;
	\end{tikzpicture}
\end{document}