exo47.tex

%@Auteur: François Meria\par
Il s'agit de construire la figure 2 ci-dessous. La figure 1
représente l'étape intermédiaire pour pouvoir construire la figure
2.
 
\begin{multicols}{2}
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\columnbreak
 
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        \pstCircleOA[linestyle=dashed]{O}{A}
        \pstInterCC[PointSymbol=none,PosAngleA=180,PointName=none]{O}{A}{A}{O}{F}{B}
        \pstInterCC[PointSymbol=none,PointNameB=none,PosAngleA=180,PointName=none]{O}{A}{F}{O}{E}{V}
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        \pstLineAB{O}{F}        \pstLineAB{O}{E}        \pstLineAB{O}{D}
        \pstLineAB{O}{C}
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        \pstLineAB{I}{B}
        \pstLineAB{B}{K}
        \pstLineAB{K}{A}
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        \pstLineAB{J}{O}
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        \pstOrtSym[PointName=none]{O}{X}{T2}[T3]
        \pstOrtSym[PointName=none]{A}{O}{T3}[T4]
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        \pspolygon[fillstyle=solid,fillcolor=red](A)(T1)(O)
        \pspolygon[fillstyle=solid,fillcolor=red](O)(T3)(D)
        \pspolygon[fillstyle=solid,fillcolor=red](B)(O)(T5)
        \pspolygon[fillstyle=solid,fillcolor=red](E)(T6)(O)
        \pspolygon[fillstyle=solid,fillcolor=red](F)(T2)(O)
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\end{center}
\end{multicols}
 
\textbf{Programme de construction }\\
 
{\texttt{Toutes les constructions doivent se faire au COMPAS
et à la règle (sans utiliser les graduations sauf pour le rayon du cercle).}}\\
 
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\begin{minipage}[c]{\textwidth}
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\textbf{\'Etape 1.}\\
Construire un cercle $\mathcal{C}$ de centre $O$ et de rayon 10~cm. Et placer un point $A$ sur le cercle $\cal C$.\\
 
\textbf{\'Etape 2.}\\
À partir du point $A$, reporter le rayon sur le cercle de manière à construire l'hexagone régulier $ABCDEF$.\\
 
\textbf{\'Etape 3.}\\
Tracer les segments $[OA]$, $[OB]$, \ldots\\
 
\textbf{\'Etape 4.}\\
Construire les médiatrices des côtés du triangle $OAB$. Elles se coupent au point $I$.\\
 
\textbf{\'Etape 5.}\\
Tracer les segments $[IA]$, $[IB]$ et $[IO]$. On obtient la figure 1.\\
 
\textbf{\'Etape 6.}\\
Recommencer les étapes précédentes dans chacun des autres triangle équilatéraux tracés.\\
 
\textbf{\'Etape 7.}\\
Colorier de trois couleurs différentes afin d'obtenir la figure 2.\\
 
\end{multicols}
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}