# index.tex

\documentclass[a4paper,11pt]{article}
\usepackage{francois_meria}
\usepackage[dvips]{graphicx}
\usepackage[dvips]{epsfig}
\setlength{\parindent}{0mm}
\lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{6\ieme}}
\pagestyle{fancy}

\begin{document}

\begin{center}
\begin{tabularx}{\textwidth}{|X|}
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\begin{center}
{\Large\textbf{Construction géométrique : \'Etoile à six branches !}}\\

\vskip 0.025cm

\end{center}\\
\hline
\end{tabularx}
\end{center}

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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\end{multicols}

\vskip 1.5cm

\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).}}\\

\vskip 0.5cm

\begin{minipage}[c]{\textwidth}
\begin{multicols}{2}\setlength{\columnseprule}{0.5pt}
\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}
\end{minipage}
}
\end{document}