\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}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{pas-math}
\usepackage[vmargin=1.5cm,rmargin=2cm,lmargin=1.5cm]{geometry}
\begin{document}
\chap[num=A,color=blue]{Courbe du Kappa}{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 de l'activité }
\begin{enumerate}
\item Se familiariser avec le vocabulaire géométrique de base
\item Tracé de droites parallèles et perpendiculaires
\item Programme de construction
\end{enumerate}
\end{bclogo}

\bigskip

\begin{pasbox}[style=act]
Toutes les constructions seront faites au crayon à papier, en traits fins et légers, sauf contre-indications.\\
\begin{enumerate}
\item  Construire une droite ($d$) horizontale sur toute la largeur de la page, puis placer un point O sur cette droite situé à peu près au milieu de la largeur de la page.
\item Construire alors la droite ($d_0$) perpendiculaire à ($d$) passant par O.
\item Tracer en pointillés vert deux droites ($d_1$) et ($d_2$) parallèles à ($d$) et situées à 3 cm d'elle, ($d_1$) étant au-dessus.\\
On note A le point d'intersection de ($d_0$) et ($d_1$).
\item On place un point P sur ($d_1$) situé à 1 cm du bord gauche de la page.
\item Tracer la droite perpendiculaire à ($d_1$) passant par P ; elle coupe ($d_2$) en un point Q.
\item Tracer le cercle de centre O et de rayon AP.
\item Tracer les segments [OP] et [OQ]. Ils coupent respectivement le cercle en M et N. On fera ces points en rouge.
\item Recommencez la construction des points M et N en prenant au début plusieurs points P espacés de 1 cm en allant vers la droite.
\end{enumerate}
\end{pasbox}

\vskip 1cm

\begin{enumerate}
\item\par~
\begin{center}
\begin{tikzpicture}
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-8.5,-4) rectangle (8.5,4.5);
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\tkzDefPoint(-7.5,3){P}
\tkzDrawPoints(P)
\tkzLabelPoints[above](P)
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-8.5,-4) rectangle (8.5,4.5);
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\tkzDefPoint(-7.5,3){P}
\tkzDrawPoints(P)
\tkzLabelPoints[above](P)
\tkzDefPoint(-8,3){X}
\tkzDefPoint(8,3){Y}
\tkzDefPoint(-8,-3){U}
\tkzDefPoint(8,-3){V}
\tkzDefLine[perpendicular=through P,K=-0.4](X,Y)\tkzGetPoint{p}
\tkzDrawLine[color=gray!20](P,p)
\tkzInterLL(P,p)(U,V)\tkzGetPoint{Q}
\tkzMarkRightAngle[color=gray!20](X,P,Q)
\tkzLabelPoints[below left](Q)
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-8.5,-4) rectangle (8.5,4.5);
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\tkzDefPoint(-7.5,3){P}
\tkzDrawPoints(P)
\tkzLabelPoints[above](P)
\tkzDefPoint(-8,3){X}
\tkzDefPoint(8,3){Y}
\tkzDefPoint(-8,-3){U}
\tkzDefPoint(8,-3){V}
\tkzDefLine[perpendicular=through P,K=-0.4](X,Y)\tkzGetPoint{p}
\tkzDrawLine[color=gray!20](P,p)
\tkzInterLL(P,p)(U,V)\tkzGetPoint{Q}
\tkzMarkRightAngle[color=gray!20](X,P,Q)
\tkzLabelPoints[below left](Q)
\tkzCalcLength[cm](A,P)\tkzGetLength{dAP}
\tkzDrawCircle[R,color=gray!50](O,\dAP cm)
\end{tikzpicture}
\end{center}

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-8.5,-4) rectangle (8.5,4.5);
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\tkzDefPoint(-7.5,3){P}
\tkzDrawPoints(P)
\tkzLabelPoints[above](P)
\tkzDefPoint(-8,3){X}
\tkzDefPoint(8,3){Y}
\tkzDefPoint(-8,-3){U}
\tkzDefPoint(8,-3){V}
\tkzDefLine[perpendicular=through P,K=-0.4](X,Y)\tkzGetPoint{p}
\tkzDrawLine[color=gray!20](P,p)
\tkzInterLL(P,p)(U,V)\tkzGetPoint{Q}
\tkzMarkRightAngle[color=gray!20](X,P,Q)
\tkzLabelPoints[below left](Q)
\tkzCalcLength[cm](A,P)\tkzGetLength{dAP}
\tkzDrawCircle[R,color=gray!50](O,\dAP cm)
\draw[gray!50] (O)--(P);
\draw[gray!50] (O)--(Q);
\tkzInterLC[R](O,P)(O,\dAP cm)\tkzGetPoints{m}{N}
\tkzDrawPoints[color=red](N)
\tkzInterLC[R](O,Q)(O,\dAP cm)\tkzGetPoints{n}{M}
\tkzDrawPoints[color=red](M)
\end{tikzpicture}
\end{center}

\newpage

\item\par~
\begin{center}
\begin{tikzpicture}
\clip (-8.5,-4) rectangle (8.5,4.5);
\draw (-8.5,0) -- (8.5,0);
\tkzDefPoint(0,0){O}
\tkzDrawPoint(O)
\tkzLabelPoints(O)
\node at (8,-0.5) {$(d)$};
\draw (0,-4) -- (0,4) node[right] {$(d_0)$};
\draw[dashed,color=green!50!black] (-8.5,3) -- (8.5,3) node[above left] {$(d_1)$};
\draw[dashed,color=green!50!black] (-8.5,-3) -- (8.5,-3) node[below left] {$(d_1)$};
\tkzDefPoint(0,3){A}
\tkzLabelPoints[above left](A)
\tkzDefPoint(-8,3){X}
\tkzDefPoint(8,3){Y}
\tkzDefPoint(-8,-3){U}
\tkzDefPoint(8,-3){V}
\foreach\x in {-7.5,-7,...,7.5}
{
\tkzDefPoint(\x,3){P}
\tkzDrawPoints(P)
\tkzLabelPoints[above](P)
\tkzDefLine[perpendicular=through P,K=-0.4](X,Y)\tkzGetPoint{p}
\tkzDrawLine[color=gray!20](P,p)
\tkzInterLL(P,p)(U,V)\tkzGetPoint{Q}
\tkzMarkRightAngle[color=gray!20](X,P,Q)
\tkzLabelPoints[below left](Q)
\tkzCalcLength[cm](A,P)\tkzGetLength{dAP}
\tkzDrawCircle[R,color=gray!20](O,\dAP cm)
\draw[gray!50] (O)--(P);
\draw[gray!50] (O)--(Q);
\tkzInterLC[R](O,P)(O,\dAP cm)\tkzGetPoints{m}{N}
\tkzDrawPoints[color=red](N)
\tkzInterLC[R](O,Q)(O,\dAP cm)\tkzGetPoints{n}{M}
\tkzDrawPoints[color=red](M)
}
\end{tikzpicture}
\end{center}
\end{enumerate}
\end{document}
