exo21.tex

%@Auteur: François Meria\par
Voici trois figures :
\begin{center}
 
\begin{pspicture}(-10,-2)(7,2)
 
    \pstGeonode[PointSymbol=+,PosAngle={-90,-45,-135}](-8,0){O_1}(-6,0){A}(-10,0){B}
    \pstCircleOA[PointSymbol=+,linecolor=red]{O_1}{A}
    \pstCurvAbsNode[PointSymbol=none]{O_1}{A}{C}{45}
    \pstLineAB[linecolor=blue]{A}{B}
    \pstLineAB[linecolor=blue]{B}{C}
    \pstLineAB[linecolor=blue]{A}{C}
\rput{15}{
    \pstGeonode[PointSymbol=+,PosAngle={-90,-45,-135}](-2,0){O_2}(0,0){D}(-4.3,0){E}
    \pstCircleOA[PointSymbol=+,linecolor=blue]{O_2}{D}
    \pstCurvAbsNode[PointSymbol=none]{O_2}{D}{F}{75}
    \pstLineAB[linecolor=red]{D}{E}
    \pstLineAB[linecolor=red]{E}{F}
    \pstLineAB[linecolor=red]{D}{F}
}
 
\rput{5}{
    \pstGeonode[PointSymbol=+,PosAngle=-90](5,0){O_3}
    \pstGeonode[PointSymbol=none,PointName=none](3,0){N}
    \pstCircleOA[PointSymbol=+]{O_3}{N}
    \pstCurvAbsNode[PointSymbol=+]{O_3}{N}{Q}{0}
    \pstCurvAbsNode[PointSymbol=+]{O_3}{N}{P}{190}
    \pstCurvAbsNode[PointSymbol=+]{O_3}{N}{R}{90}
    \pstLineAB[linecolor=blue]{P}{Q}
    \pstLineAB[linecolor=blue]{Q}{R}
    \pstLineAB[linecolor=blue]{R}{P}
}
\end{pspicture}
\end{center}
Sans utiliser le moindre instrument de géométrie, les triangles
suivants sont-ils rectangles ? ($O_1$, $O_2$ et $O_3$ sont les centres
des cercles).