# 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}

\makeatletter
% use transpalpha=<mumber> to the the opacity level
\define@key[psset]{}{transpalpha}{\pst@checknum{#1}\pstranspalpha}
\psset{transpalpha=1}
\def\psfs@transp{%
\psfs@solid}
\makeatother

\begin{document}

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

\vskip 0.1cm
\begin{center}
{\Large\textbf{Construction géométrique : Triangles et cercles !}}\\

\vskip 0.025cm

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

\vskip 0.55cm

Il s'agit de construire la figure 2 ci-dessous.

\begin{multicols}{2}
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\pstMiddleAB[PointSymbol=none,PosAngle=-90]{B}{C}{J}
\pstMiddleAB[PointSymbol=none,PosAngle=45]{A}{C}{K}
\pstMiddleAB[PointSymbol=none,PosAngle=135]{B}{A}{I}
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\put(5,-3.8){Figure $1$}
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\end{center}

\columnbreak

\begin{center}
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\pstMiddleAB[PointSymbol=none,PosAngle=45,PointName=none]{A}{C}{K}
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\pstInterLL[PointName=none,PointSymbol=none]{A}{J}{B}{K}{O}
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\pstArcOAB[linewidth=1.5pt]{F}{A}{C}
\pstArcOAB[linewidth=1.5pt]{J}{C}{B}
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\put(5,-3.8){Figure $2$}
\endpspicture
\end{center}
\end{multicols}
\vskip 1.5cm

\textbf{\LARGE Programme de construction }\\

\large{\texttt{Toutes les constructions doivent se faire à
l'équerre, à la règle et au compas.}}\\

\vskip 0.5cm

\begin{minipage}[c]{\textwidth}
\begin{multicols}{2}\setlength{\columnseprule}{0.5pt}
\textbf{\'Etape 1.}\\
Tracer un triangle équilatéral $ABC$ de côté 12~cm et repérer les milieux $I$, $J$ et $K$ de chaque côté.\\

\textbf{\'Etape 2.}\\
Tracer les cercles de diamètres les côtés du triangle $ABC$.\\

\textbf{\'Etape 3.}\\
Tracer les segments joingant chaque sommet du triangle au milieu du côté opposé. On parle de médianes du triangle.\\
Prolonger ces médianes de 2~cm ; on obtient les points $D$, $E$ et
$F$.\\
\textbf{\'Etape 4.}\\
Tracer les perpendiculaires à ces médianes passant par les
points $D$, $E$ et $F$. On obtient un nouveau triangle $A'B'C'$.\\

\textbf{\'Etape 5.}\\
Tracer des arcs de cercles ayant pour centre $D$, $E$ et $F$ et passant respectivement par $B$ et $C$,
$A$ et $B$ et $A$ et $C$.\\

\textbf{\'Etape 6.}\\
Colorier la figure en alternant deux couleurs.\\
\end{multicols}
\end{minipage}
}
\end{document}