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\lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{6\ieme}}
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\rhead{\textit{Année} 2005/2006}
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{\Large\textbf{Construction géométrique : \'Etoile à six branches !}}\\
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Il s'agit de construire la figure 2 ci-dessous. La figure 1
représente l'étape intermédiaire pour pouvoir construire la figure
2.
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\textbf{\LARGE Programme de construction }\\
\large{\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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\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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}
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