\documentclass[a4paper]{article}%
\usepackage{amsfonts}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{amsmath,amssymb}
\usepackage[a4paper]{geometry}
\usepackage{xspace}
\usepackage{fancyhdr}
\usepackage{enumerate}
\usepackage{multicol}
\usepackage{theorem}
\usepackage{graphics}
\usepackage{graphicx}
\usepackage{lastpage}
\usepackage[french]{layout}
\usepackage{boxedminipage}
\usepackage{fancybox}
\usepackage{sectsty}
\usepackage{array}
\usepackage[french]{babel}%
\usepackage{amsmath}%
\setcounter{MaxMatrixCols}{30}%
\usepackage{amssymb}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.00.0.2552}
%TCIDATA{CSTFile=40 LaTeX article.cst}
%TCIDATA{LastRevised=Thursday, September 02, 2004 18:57:26}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
\geometry{a4paper,marginpar=2cm,lmargin=0cm,rmargin=2cm,marginparsep=0pt,includemp=true,reversemp=true,headsep=-0.2in}
\setlength{\theorempostskipamount}{2\baselineskip}
\theoremheaderfont{\large\bfseries}
{\theorembodyfont{\large\upshape\mdseries}\theoremstyle{break}
\newtheorem{theorem}{Théorème}
}
\newcounter{Cack}[section]
{\theorembodyfont{\large\upshape}\theoremstyle{break}
\newtheorem{acknowledgement}[Cack]{A savoir}
}
\newcounter{Calg}[section]
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{algorithm}[Calg]{Méthode}
}
\newcounter{Caxi}[section]
{\theorembodyfont{\itshape}
\newtheorem{axiom}[Caxi]{Axiome}
}
\newcounter{Ccas}[section]
{\theorembodyfont{\upshape}
\newtheorem{case}[Ccas]{Cas}
}
\newcounter{Ccorr}[section]
\renewcommand{\theCcorr}{\Roman{Ccorr}}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{claim}[Ccorr]{Correction de l'exercice}
}
\newcounter{Cconc}[theorem]
{\theorembodyfont{\large\mdseries}
\newtheorem{conclusion}[Cconc]{Conclusion}
}
\newcounter{Ccond}[theorem]
{\theorembodyfont{\large\mdseries}
\newtheorem{condition}[Ccond]{Hypothèse}
}
\newcounter{Cconj}[section]
{\theorembodyfont{\upshape}
\newtheorem{conjecture}[Cconj]{Conjecture}
}
\newcounter{Ccor}[section]
{\theorembodyfont{\upshape}
\newtheorem{corollary}[Ccor]{Corollaire}
}
\newcounter{Ccrit}[section]
{\theorembodyfont{\upshape}
\newtheorem{criterion}[Ccrit]{Critère}
}
\newcounter{Cdef}[section]
\newcounter{Cnot}[section]
{\theorembodyfont{\large\upshape}\theoremstyle{break}
\newtheorem{definition}[Cdef]{Définition}
\newtheorem{notation}[Cnot]{Notation}
}
\newcounter{Cexa}[section]
{\theorembodyfont{\slshape}
\newtheorem{example}[Cexa]{Exemple}
}
\newcounter{Cexe}[section]
\renewcommand{\theCexe}{\Roman{Cexe}}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{exercise}[Cexe]{Exercice}
}
\newcounter{Clem}[section]
{\theorembodyfont{\upshape}
\newtheorem{lemma}[Clem]{Lemme}
}
\newcounter{Cprob}[section]
\renewcommand{\theCprob}{\Roman{Cprob}.}
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{problem}[Cprob]{Problème}
}
{\theorembodyfont{\large\mdseries}\newcounter{Cprop}[section]\theoremstyle{break}
\newtheorem{proposition}[Cprop]{Propriété}
}
\newcounter{Crem}[section]
{\theorembodyfont{\itshape}
\newtheorem{remark}[Crem]{Remarque}
}
\newcounter{Csol}[section]
{\theorembodyfont{\upshape}\theoremstyle{break}
\newtheorem{solution}[Csol]{Solution}
}
\newcounter{Csum}[section]{\theorembodyfont{\upshape}
\newtheorem{summary}[Csum]{En résumé}
}
\newenvironment{proof}[1][Démonstration]{\noindent\textbf{#1:}}{\ \fbox{cqfd.}}
\renewcommand{\theenumi}{\arabic{enumi}}
\renewcommand{\theenumii}{\alph{enumii}}
\renewcommand{\theenumiii}{\roman{enumiii}}
\renewcommand{\labelenumi}{\textbf{\theenumi)}}
\renewcommand{\labelenumii}{\textbf{\theenumii)}}
\renewcommand{\labelenumiii}{\textbf{\theenumiii.}}
\newcommand{\LeTitre}{}
\newcommand{\Titre}[1]{\title{#1}\renewcommand{\LeTitre}{#1}}
\newcommand{\LaClasse}{}
\newcommand{\Classe}[1]{\renewcommand{\LaClasse} {#1}}
\newcommand{\LaDate}{}
\newcommand{\Date}[1]{\author{#1}\renewcommand{\LaDate} {#1}}
\newcommand{\Duree}[1]{\date{#1}}
\newcommand{\Letablissement}{}
\newcommand{\Etablissement}[1]{\renewcommand{\Letablissement} {#1}}
\newcommand{\Ladiscipline}{}
\newcommand{\Discipline}[1]{\renewcommand{\Ladiscipline}{#1}}
\renewcommand{\thesection}{\Alph{section}}
\renewcommand{\thesubsection}{\thesection\arabic{subsection}}
\renewcommand{\thesubsubsection}{\thesubsection.\arabic{subsubsection}}
\newcounter{exo}
\newcommand{\exo}[1][-]{\stepcounter{exo}\par\vspace{2ex}\noindent{\bf Exercice \theexo\space}\points{#1}\\[1ex]\noindent}
\newcommand{\GN}{\ensuremath{\mathbb{N}}\xspace}
\newcommand{\GR}{\ensuremath{\mathbb{R}}\xspace}
\newcommand{\GC}{\ensuremath{\mathbb{C}}\xspace}
\newcommand{\GZ}{\ensuremath{\mathbb{Z}}\xspace}
\newcommand{\GQ}{\ensuremath{\mathbb{Q}}\xspace}
\newcommand{\GD}{\ensuremath{\mathbb{D}}\xspace}
\newcommand{\ssi}{\ensuremath{\Longleftrightarrow}}
\newcommand{\vecteur}[1]{\overrightarrow{#1\;}}
\newcommand{\oij}{(O;\vecteur{\imath},\vecteur{\jmath})}
\newcommand{\oijk}{\left(O;\vecteur{i},\vecteur{j},\vecteur{k}\right)}
\newcommand{\ouv}{\left(O;\vecteur{u},\vecteur{v}\right)}
\newcommand{\congru}[3]{#1\equiv#2\quad\text{modulo }#3}
\newcommand{\segN}[2]{\left\{ #1\ldots #2\right\}}
\newcommand{\anglevec}[2]{\left(\vecteur{#1};\vecteur{#2}\right)}
\newcommand{\PGCD}{\mathit{PGCD}}
\newcommand{\aire}[1]{\mathcal{A}ire(#1)}
\newcommand{\Mod}{\quad\mathit{Mod}}
\newcommand{\Intoo}[2]{\left]#1;#2\right[}
\newcommand{\Intfo}[2]{\left[#1;#2\right[}
\newcommand{\Intof}[2]{\left]#1;#2\right]}
\newcommand{\Intff}[2]{\left[#1;#2\right]}
\newcommand{\Lim}[1]{\underset{#1}{\lim }}
\newenvironment{listerd}
{   \renewcommand{\labelitemi}{\textasteriskcentered}
\renewcommand{\labelitemii}{\textperiodcentered}
\begin{itemize}
}{\end{itemize}}
\newenvironment{qcm}
{   \renewcommand{\labelitemi}{{\setlength{\fboxrule}{.05em}\setlength{\fboxsep}{0pt}\fbox{\rule[-0.3em]{0pt}{1em}\hspace{1em}}}}
\begin{itemize}
}{\end{itemize}}
\newcommand{\cro}{
\parbox{1.4cm}{
\setlength{\unitlength}{0.1cm}
\begin{picture}(14,7)
\put(0,0){\vector(2,1){14}}
\end{picture}
}
}
\newcommand{\dec}{
\parbox{1.4cm}{
\setlength{\unitlength}{0.1cm}
\begin{picture}(14,7)
\put(0,7){\vector(2,-1){14}}
\end{picture}
}
}
\everymath{\displaystyle}
\def \points#1%
{\if -#1 \xspace \else {\small ( #1 points )}\xspace\fi }
\DeclareMathOperator{\e}{e}
\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 129942649103663--
%%--Fonctions liées à une configuration plane--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
\hfill%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{11cm}}}%
%BeginExpansion
\begin{minipage}{11cm}%
%EndExpansion
$ABCD$ est trapèze rectangle tel que:
\[
AB=6\quad,\quad CD=2\quad,\quad AD=4
\]
$M$ est un point du segment $[AD]$. On pose $AM=x$.

On construit le rectangle $AMNP$ inscrit dans $ABCD$ comme sur la figure
ci-contre.
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
\hfill%
%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{5.2cm}}}%
%BeginExpansion
\begin{minipage}{5.2cm}%
%EndExpansion%
%TCIMACRO{\FRAME{itbpF}{2.1229in}{1.5176in}{0in}{}{}{fig.eps}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 2.1229in;  height 1.5176in;  depth 0in;  original-width 1.9992in;
%original-height 1.4213in;  cropleft "0";  croptop "1";  cropright "1";
%cropbottom "0";  filename 'Include/fig.eps';file-properties "XNPEU";}}}%
%BeginExpansion
{\includegraphics[
height=1.5176in,
width=2.1229in
]%
{Include/i3fb3q1n.eps}%
}%
%EndExpansion
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{Partie}{\subsection*{Partie A}}}%
%BeginExpansion
\subsection*{Partie A}%
%EndExpansion


\begin{enumerate}
\item Construire la figure pour $x=3$, en prenant pour unité de longueur le cm.

\item Dans quel intervalle se trouvent les différentes valeurs possibles de
$x$? On note $I$ cet intervalle.

\item Soit $H$ le projeté orthogonal de $C$ sur $[AB]$.

En utilisant le théorème de Thalès, démontrer que $BP=2$.%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{9.5cm}}}%
%BeginExpansion
\begin{minipage}{9.5cm}%
%EndExpansion


\vspace{5pt}

\hspace{0pt}
%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{9.5cm}}}%
%BeginExpansion
\begin{minipage}{9.5cm}%
%EndExpansion


On peut donc à présent reporter toutes les informations concernant les
longueurs de la figure (voir ci-contre).%
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion


\vspace{5pt}

\item Exprimer $AP$ en fonction de $x$.

\item En déduire que l'expression de l'aire de $AMNP$ en fonction de~$x$ est:
\[
\mathcal{A}ire(AMNP)=6x-x^{2}%
\]%
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
\hfill%
%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{6cm}}}%
%BeginExpansion
\begin{minipage}{6cm}%
%EndExpansion%
%TCIMACRO{\FRAME{itbpF}{6.0711cm}{5.2613cm}{0cm}{}{}{fig_anot.eps}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 6.0711cm;  height 5.2613cm;  depth 0cm;  original-width 2.2515in;
%original-height 1.956in;  cropleft "0";  croptop "1";  cropright "1.0036";
%cropbottom "0";  filename 'Include/fig_anot.eps';file-properties "XNPEU";}}}%
%BeginExpansion
\raisebox{-0cm}{\includegraphics[
trim=0.000000in 0.000000in -0.008105in 0.000000in,
height=5.2613cm,
width=6.0711cm
]%
{Include/i3fb3q1p.eps}%
}%
%EndExpansion
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion

\end{enumerate}%

%TCIMACRO{\TeXButton{Partie}{\subsection*{Partie B}}}%
%BeginExpansion
\subsection*{Partie B}%
%EndExpansion


On note $f$ la fonction définie sur l'intervalle $[0;4]$ par $f(x)=6x-x^{2}$.

\begin{enumerate}
\item Compléter le tableau de valeurs \ref{2401021215} de la page
\pageref{2401021215}.

\item Tracer la courbe représentative de la fonction $f$ dans le repère de la
figure \ref{2401021221} page \pageref{2401021221}.

\item Démontrer que que l'expression de l'aire du triangle $ADP$ en fonction
de~$x$ est:
\[
\mathcal{A}ire(ADP)=12-2x
\]


\item
\begin{enumerate}
\item Tracer sur le graphique \ref{2401021221} page \pageref{2401021221} la
représentation de la fonction $x\mapsto12-2x$ pour $x$ élément de l'intervalle
$[0;4]$.

\item Lire sue ce graphique les coordonnées du point $K$ d'intersection des
deux courbes.

\item Quels renseignements les coordonnées de ce point donnent-elles à propos
des aires de $ADP$ et de $AMNP$?
\end{enumerate}
\end{enumerate}%

%TCIMACRO{\TeXButton{Partie}{\subsection*{Partie C}}}%
%BeginExpansion
\subsection*{Partie C}%
%EndExpansion


On se propose de déterminer par le calcul la valeur de $x$ pour laquelle les
aires de $ADP$ et de $AMNP$ sont égales.

\begin{enumerate}
\item \label{C1_iei}Écrire l'équation permettant de calculer cette valeur.

\item Développer l'expression $(x-4)^{2}-4$.

\item En déduire la résolution de l'équation de \textbf{C--\ref{C1_iei}.}. Conclure.
\end{enumerate}

\vspace{\stretch{2}}

\begin{table}[p]
\begin{center}
%Pour visualiser ce tableau il faut ajouter le paquetage "array".%
\begin{tabular}
[c]{|c|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|}\hline
$x$ & $0$ & $0,5$ & $1$ & $1,5$ & $2$ & $2,5$ & $3$ & $3,5$ & $4$\\\hline
$f(x)${\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-3mm]{0pt}{7mm}}} & \multicolumn{1}{|c|}{} &
\multicolumn{1}{|c|}{} & \multicolumn{1}{|c|}{} & \multicolumn{1}{|c|}{} &
\multicolumn{1}{|c|}{} & \multicolumn{1}{|c|}{} & \multicolumn{1}{|c|}{} &
\multicolumn{1}{|c|}{} & \multicolumn{1}{|c|}{}\\\hline
\end{tabular}
\end{center}
\caption{{}}%
\label{2401021215}%
\end{table}%

%TCIMACRO{\FRAME{fpF}{3.7227in}{5.32in}{0pt}{}{\Qlb{2401021221}}{repere.eps}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 3.7227in;  height 5.32in;  depth 0pt;  original-width 3.5276in;
%original-height 5.0527in;  cropleft "0";  croptop "1";  cropright "1";
%cropbottom "0";  filename 'Include/repere.eps';file-properties "XNPEU";}}}%
%BeginExpansion
\begin{figure}
[p]
\begin{center}
\includegraphics[
height=5.32in,
width=3.7227in
]%
{Include/i3fb3q1r.eps}%
\label{2401021221}%
\end{center}
\end{figure}
%EndExpansion
%\begin{pspicture}(-.5,-.5)(8.5,12.5)
%\newrgbcolor{gris}{.7 .7 .7}
%\psgrid[gridlabels=0,subgriddiv=5,subgridwidth=0.1pt,
%subgriddots=0,gridwidth=0.2pt,griddots=0,subgridcolor=gris,unit=.5]%
%(0,0)(0,0)(16,24)
%\psset{xunit=2}
%\psaxes[linewidth=0.6pt]{->}(0,0)(-0.25,-0.5)(4.25,12.5)
%\uput{.2cm}[225](0,0){$0$}
%\uput[-90](4.25,0){$x$}
%\uput[0](0,12.5){$y$}
%\end{pspicture}

\end{exercise}


\end{document}