# exo43.tex

%@Auteur:Arnaud Gazagnes\par
\begin{enumerate}
\item Donner la propri\'et\'e de l'in\'egalit\'e triangulaire.
\item Indiquer, pour chaque triangle, le nom des droites repr\'esent\'ees.

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\pstLineAB{A}{B}\pstLineAB{A}{C}\pstLineAB{B}{C}
\pstProjection{B}{C}{A}[H_A]
\pstLineAB[nodesepA=-5,nodesepB=-5]{A}{H_A}
\pstProjection{A}{C}{B}[H_B]
\pstLineAB[nodesepA=-5,nodesepB=-5]{B}{H_B}
\pstProjection{A}{B}{C}[H_C]
\pstLineAB[nodesepA=-5,nodesepB=-5]{C}{H_C}
\pstInterLL[PosAngle=290]{A}{H_A}{B}{H_B}{H}
\pstRightAngle{H}{H_A}{C}
\pstRightAngle{H}{H_B}{A}
\pstRightAngle{H}{H_C}{B}
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\hfill
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\pstMiddleAB[PosAngle=140]{A}{B}{C'}
\pstMiddleAB[PosAngle=2405]{A}{C}{B'}
\pstMiddleAB[PosAngle=270]{B}{C}{A'}
\pstInterLL{A}{A'}{B}{B'}{G}
\pstSegmentMark[SegmentSymbol=MarkHash]{A}{C'} \pstSegmentMark[SegmentSymbol=MarkHash]{B}{C'}
\pstSegmentMark[SegmentSymbol=MarkHashh]{B}{A'} \pstSegmentMark[]{C}{A'}
\pstSegmentMark[SegmentSymbol=MarkHashhh]{C}{B'} \pstSegmentMark[SegmentSymbol=MarkHashhh]{A}{B'}
\pstLineAB[nodesepA=-5,nodesepB=-5]{A}{A'}
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\pstLineAB{A}{B}\pstLineAB{A}{C}\pstLineAB{B}{C}
{\psset{CodeFig=true,CodeFigColor=black,nodesepA=-15,nodesepB=-5,PointSymbolB=none}\pstMediatorAB[SegmentSymbol=MarkHash]{C}{B}{A'}{M_A}
\pstMediatorAB{B}{A}{C'}{M_C}
\pstMediatorAB[SegmentSymbol=MarkHashhh]{A}{C}{B'}{M_B}}
\pstInterLL{A'}{M_A}{B'}{M_B}{O}
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\item Donner la d\'efinition d'une\dots
\begin{enumerate}
\item m\'ediatrice
\item m\'ediane
\item hauteur
\end{enumerate}
\item A quel type de droites est li\'e le centre du cercle circonscrit ?
\end{enumerate}