\documentclass[12pt]{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[francais]{babel}
\usepackage{lmodern}
\usepackage[colorlinks=true,urlcolor=blue!50!black, linkcolor=blue!50!black]{hyperref}
\usepackage{pas-cours}
\usepackage[tikz]{bclogo}
\usepackage{mathrsfs}
\usepackage{tkz-euclide}
\usepackage{pas-math}
\usepackage[vmargin=1.5cm,rmargin=2cm,lmargin=1.5cm]{geometry}
\begin{document}
\chap[num=A,color=blue]{Construction d'une étoile à 5 branches}{Stéphane PASQUET, \today, \url{http://www.mathweb.fr}}

\itemclass{blue}
\begin{bclogo}[%
	couleur=blue!20,%
	couleurBord=blue!50!black,%
	arrondi=0.1,%
	logo=\bcquestion,%
	ombre=true,%
	couleurOmbre=blue!50!black!50,%
	blur,%
	barre=snake]{Intér\^ets des activités}
\begin{enumerate}
\item Manipulation du compas
\item Tracé de médiatrices et de perpendiculaires
\item Programme de construction
\end{enumerate}
\end{bclogo}

\bigskip

\begin{pasbox}[degrade,style=act]
\begin{enumerate}
\item  Trace un cercle $\mathscr{C}$ de rayon 4 cm et de centre O.\\
Trace ensuite deux diamètres perpendiculaires ; on les nommera [AB] et [CD].
\item Place le point I milieu de [AO].
\item Trace l'arc de cercle de centre I et de rayon CI en partant du point C jusqu'au segment [OB]. On notera M l'intersection de [OB] et de cet arc de cercle.
\item Place le point J milieu de [OM].
\item Trace la perpendiculaire à [AB] passant par J. Elle coupe $\mathscr{C}$ en deux points E et F.
\item Construit maintenant les points G et H sur $\mathscr{C}$ tels que EB = EG et FB = FH.
\item Trace le cercle $\mathscr{C}^\prime$ de centre O et de rayon OJ.\\
Trace ensuite les segments [BE], [EG], [GH], [HF] et [FB].
\item Trace les médiatrices de chacun de ces segments ; elles coupent $\mathscr{C}^\prime$ respectivement en b, e, g, h et f.
\item Tu peux maintenant joindre les points B, b, E, e, G, g, H, h, F et f pour obtenir ton étoile !
\end{enumerate}
\end{pasbox}

\newpage

\begin{enumerate}
\item\par~
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(A,B)
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(A,B)
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(A,B)
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\tkzInterLC(O,B)(I,C)\tkzGetPoints{N}{M}
\tkzDrawArc[rotate,dashed,color=gray!50](I,C)(-63.5)
\tkzDrawPoint(M)
\tkzLabelPoint[below](M){M}
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(A,B)
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\tkzInterLC(O,B)(I,C)\tkzGetPoints{N}{M}
\tkzDrawArc[rotate,dashed,color=gray!50](I,C)(-63.5)
\tkzDrawPoint(M)
\tkzLabelPoint[below](M){M}
\tkzDefMidPoint(O,M)\tkzGetPoint{J}\tkzDrawPoint(J)
\tkzLabelPoint[below](J){J}
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-4.5,-4.5) rectangle (4.5,4.5);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\tkzInterLC(O,B)(I,C)\tkzGetPoints{N}{M}
\tkzDrawArc[rotate,dashed,color=gray!50](I,C)(-63.5)
\tkzDrawPoint(M)
\tkzLabelPoint[below](M){M}
\tkzDefMidPoint(O,M)\tkzGetPoint{J}\tkzDrawPoint(J)
\tkzLabelPoint[below](J){J}
\tkzDefLine[perpendicular=through J,K=0.5](A,B)\tkzGetPoint{j}
\tkzInterLC(J,j)(O,B)\tkzGetPoints{E}{F}
\tkzDrawLine[color=green!20](E,F)
\tkzMarkRightAngle[color=green!20](B,J,E)
\tkzLabelPoint[below](F){F}
\tkzLabelPoint[above](E){E}
\tkzDrawSegment(A,B)
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-4.5,-4.5) rectangle (4.5,4.5);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\tkzInterLC(O,B)(I,C)\tkzGetPoints{N}{M}
\tkzDrawArc[rotate,dashed,color=gray!50](I,C)(-63.5)
\tkzDrawPoint(M)
\tkzLabelPoint[below](M){M}
\tkzDefMidPoint(O,M)\tkzGetPoint{J}\tkzDrawPoint(J)
\tkzLabelPoint[below](J){J}
\tkzDefLine[perpendicular=through J,K=0.5](A,B)\tkzGetPoint{j}
\tkzInterLC(J,j)(O,B)\tkzGetPoints{E}{F}
\tkzDrawLine[color=green!20](E,F)
\tkzMarkRightAngle[color=green!20](B,J,E)
\tkzLabelPoint[below](F){F}
\tkzLabelPoint[above](E){E}
\tkzDrawSegment(A,B)
\tkzCalcLength[cm](E,B)\tkzGetLength{dEB}
\tkzInterCC[R](O,4 cm)(E,\dEB cm)\tkzGetPoints{G}{B}
\tkzCompass(E,G)
\tkzLabelPoint[left](G){G}
\draw[red] (E) -- (G) node[midway,rotate=90] {$\equiv$};
\draw[red] (E) -- (B) node[midway] {$\equiv$};
%
\tkzInterCC[R](O,4 cm)(F,\dEB cm)\tkzGetPoints{B}{H}
\tkzCompass(F,H)
\tkzLabelPoint[left](H){H}
\draw[red] (F) -- (B) node[midway] {$\equiv$};
\draw[red] (F) -- (H) node[midway,rotate=90] {$\equiv$};
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-4.5,-4.5) rectangle (4.5,4.5);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoint(O){O}
\tkzDrawCircle[R](O,4 cm)
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(0,4){C}
\tkzDefPoint(0,-4){D}
\tkzDrawSegment(C,D)
\tkzLabelPoint[above](C){C}
\tkzLabelPoint[right](B){B}
\tkzLabelPoint[left](A){A}
\tkzLabelPoint[below](D){D}
\tkzDefMidPoint(A,O)\tkzGetPoint{I}
\tkzDrawPoint(I)
\tkzLabelPoint[below](I){I}
\tkzInterLC(O,B)(I,C)\tkzGetPoints{N}{M}
\tkzDrawArc[rotate,dashed,color=gray!50](I,C)(-63.5)
\tkzDrawPoint(M)
\tkzLabelPoint[below](M){M}
\tkzDefMidPoint(O,M)\tkzGetPoint{J}\tkzDrawPoint(J)
\tkzLabelPoint[below](J){J}
\tkzDefLine[perpendicular=through J,K=0.5](A,B)\tkzGetPoint{j}
\tkzInterLC(J,j)(O,B)\tkzGetPoints{E}{F}
\tkzDrawLine[color=green!20](E,F)
\tkzMarkRightAngle[color=green!20](B,J,E)
\tkzLabelPoint[below](F){F}
\tkzLabelPoint[above](E){E}
\tkzDrawSegment(A,B)
\tkzCalcLength[cm](E,B)\tkzGetLength{dEB}
\tkzInterCC[R](O,4 cm)(E,\dEB cm)\tkzGetPoints{G}{B}
\tkzLabelPoint[left](G){G}
\tkzInterCC[R](O,4 cm)(F,\dEB cm)\tkzGetPoints{B}{H}
\tkzLabelPoint[left](H){H}
\tkzDrawCircle[color=gray!20](O,J)
\tkzDrawSegments[gray!50](B,E E,G G,H  H,F F,B)
%
\tkzDefLine[mediator](B,E)\tkzGetPoints{bb}{ee}
\tkzDrawLine[dotted,color=gray!20](bb,ee)
\tkzInterLC(bb,ee)(O,J)\tkzGetPoints{bbb}{b}
\tkzDrawPoint(b)\tkzLabelPoint[above right](b){b}
%
\tkzDefLine[mediator](E,G)\tkzGetPoints{ee}{gg}
\tkzDrawLine[dotted,color=gray!20](ee,gg)
\tkzInterLC(ee,gg)(O,J)\tkzGetPoints{eee}{e}
\tkzDrawPoint(e)\tkzLabelPoint[above](e){e}
%
\tkzDefLine[mediator](G,H)\tkzGetPoints{gg}{hh}
%\tkzDrawLine[dotted,color=gray!20](gg,hh)
\tkzInterLC(gg,hh)(O,J)\tkzGetPoints{ggg}{g}
\tkzDrawPoint(g)\tkzLabelPoint[above left](g){g}
\end{tikzpicture}
\end{center}
\end{enumerate}
\end{document}