# index.tex

\documentclass[a4paper,11pt]{article}
\usepackage{francois_meria}
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\lhead{\textsf{Collège Château Forbin} - \textit{Mathématiques} - \textsf{6\ieme}}
\pagestyle{fancy}

\begin{document}

\begin{center}
\begin{tabularx}{\textwidth}{|X|}
\hline

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\begin{center}
{\Large\textbf{Construction géométrique d'un Pentagramme}}\\

\vskip 0.025cm

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

\vskip 0.55cm

\begin{multicols}{2}\setlength{\columnseprule}{0.5pt}
L'étoile ci-contre s'appelle un \textit{pentagramme}.\\
On veut réaliser la construction d'un pentagramme en partant d'un
cercle de rayon 8~cm.\\
Pour cela, la réalisation passera par les sept étapes de
construction décrites plus bas.

\columnbreak

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\textbf{\'Etapes de la construction}.

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\textbf{\'Etape 1.}
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\textbf{\'Etape 2.}
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\textbf{\'Etape 3.}
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\textbf{\'Etape 4.}
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\textbf{\'Etape 5.}
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\textbf{\'Etape 6.}
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%%%%%%% figure 7
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\vskip 0.3cm

\textbf{\'Etape 7.}
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\newpage
\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 l'étape 1).}}\\

\vskip 2.5cm

\begin{minipage}[c]{\textwidth}
\textbf{\'Etape 1.}\\
Construire un cercle $\mathcal{C}$ de centre $O$ et de diamètre
horizontal $[DD']$ tel que $DD'=16~$cm.\\

\textbf{\'Etape 2.}\\
Construire la médiatrice du segment $[DD']$. Nommer $A$ le point
du cercle au Nord, c'est-à-dire sur le cercle, sur la médiatrice
de $[DD']$ en haut du cercle.\\

\textbf{\'Etape 3.}\\
Construire la médiatrice du segment $[OD']$ et nommer $B$ le
milieu du $[OD']$.\\
Tracer le segment $[AB]$ en pointillés.\\

\textbf{\'Etape 4.}\\
Tracer le cercle de centre $B$ passant par $A$ et nommer $E$ le
point d'intersection du segment $[DO]$ et de ce cercle.\\

\textbf{\'Etape 5.}\\
Tracer le cercle de centre $A$ et de rayon $[AE]$. Il coupe le
cercle $\mathcal{C}$ de départ en $A_1$ et $A_4$.\\

\textbf{\'Etape 6.}\\
Le cercle de centre $A_1$ passant par $A$ recoupe le cercle ${\cal C}$ en $A_2$.\\
Le cerlce de centre $A_4$ passant par $A$ recoupe le cercle ${\cal C}$ en $A_3$.\\

\textbf{\'Etape 7.}\\
Tracer le polygone $AA_2A_4A_1A_3$ puis effacer les traits de
construction. Enfin colorier le \textit{pentagramme} ainsi obtenu.
\end{minipage}
}
\end{document}