\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}} \chead{} \rhead{\textit{Année} 2005/2006} \pagestyle{fancy} \renewcommand{\headrulewidth}{0.5pt} \begin{document} \begin{center} \begin{tabularx}{\textwidth}{|X|} \hline \vskip 0.1cm \begin{center} {\Large\textbf{Construction géométrique : Cercles et sphère !}}\\ \vskip 0.025cm \end{center}\\ \hline \end{tabularx} \end{center} \begin{center} \psset{unit=0.75cm} \pspicture(-9,-10.4)(9,7) \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,0){O} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,-2){N} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,0.3){O_1} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,0.6){O_2} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,0.9){O_3} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,1.2){O_4} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,1.5){O_5} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,1.8){O_6} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,2.1){O_7} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,2.4){O_8} \pstGeonode[PointSymbol=none,PosAngle={90},PointName=none](0,6.8){P} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,2.1){Q} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,1.8){K_1} \pstGeonode[PointSymbol=none,PosAngle={0},PointName=none](0,1.5){K_2} \pstGeonode[PointSymbol=none,PosAngle={1},PointName=none](0,1.2){K_3} \pstGeonode[PointSymbol=none,PosAngle={2},PointName=none](0,0.9){K_4} \pstGeonode[PointSymbol=none,PosAngle={3},PointName=none](0,0.6){K_5} \pstGeonode[PointSymbol=none,PosAngle={4},PointName=none](0,0.3){K_6} \pstGeonode[PointSymbol=none,PosAngle={5},PointName=none](0,0){K_7} \pstGeonode[PointSymbol=none,PosAngle={6},PointName=none](0,-0.3){K_8} \pstGeonode[PointSymbol=none,PosAngle={7},PointName=none](0,-0.6){K_9} \pstGeonode[PointSymbol=none,PosAngle={8},PointName=none](0,-0.9){L_1} \pstGeonode[PointSymbol=none,PosAngle={9},PointName=none](0,-1.2){L_2} \pstGeonode[PointSymbol=none,PosAngle={10},PointName=none](0,-1.5){L_3} \pstGeonode[PointSymbol=none,PosAngle={11},PointName=none](0,-1.8){L_4} \pstGeonode[PointSymbol=none,PosAngle={12},PointName=none](0,-2.1){L_5} \pscircle[fillstyle=solid,fillcolor=black](L_4){8.6} \pscircle[fillstyle=solid,fillcolor=white](L_3){8.3} \pscircle[fillstyle=solid,fillcolor=black](L_2){8} \pscircle[fillstyle=solid,fillcolor=white](L_1){7.7} \pscircle[fillstyle=solid,fillcolor=black](K_9){7.4} \pscircle[fillstyle=solid,fillcolor=white](K_8){7.1} \pscircle[fillstyle=solid,fillcolor=black](K_7){6.8} \pscircle[fillstyle=solid,fillcolor=white](K_6){6.5} \pscircle[fillstyle=solid,fillcolor=black](K_5){6.2} \pscircle[fillstyle=solid,fillcolor=white](K_4){5.9} \pscircle[fillstyle=solid,fillcolor=black](K_3){5.6} \pscircle[fillstyle=solid,fillcolor=white](K_2){5.3} \pscircle[fillstyle=solid,fillcolor=black](K_1){5} \pscircle[fillstyle=solid,fillcolor=white](Q){4.7} \pscircle[fillstyle=solid,fillcolor=black](O_8){4.4} \pscircle[fillstyle=solid,fillcolor=white](O_7){4.1} \pscircle[fillstyle=solid,fillcolor=black](O_6){3.8} \pscircle[fillstyle=solid,fillcolor=white](O_5){3.5} \pscircle[fillstyle=solid,fillcolor=black](O_4){3.2} \pscircle[fillstyle=solid,fillcolor=white](O_3){2.9} \pscircle[fillstyle=solid,fillcolor=black](O_2){2.6} \pscircle[fillstyle=solid,fillcolor=white](O_1){2.3} \pscircle[fillstyle=solid,fillcolor=black](O){2} \endpspicture \end{center} \vskip 0.15cm \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 reporter les longueurs).}}\\ \vskip 0.5cm \shadowbox{ \begin{minipage}[c]{\textwidth} \begin{multicols}{2}\setlength{\columnseprule}{0.5pt} \textbf{\'Etape 1.}\\ Construire une droite $(d)$ verticale au centre de la feuille, et placer un point $O$ sur cette droite.\\ \textbf{\'Etape 2.}\\ Tracer le cercle ${\cal C}$ de centre $O$ et de rayon $2$~cm. Le point au sud de $O$ à l'intersection de ${\cal C}$ et $(d)$ est noté $N$.\\ \textbf{\'Etape 3.}\\ Placer les points $O_1$, $O_2$, \ldots, $O_8$ au dessus de $O$ sur la droite $(d)$, espacés de $3$~mm. Tracer les cercles ayant ces points comme centre et passant par $N$. Le dernier cercle de centre $O_8$ recoupe la droite $(d)$ au point $P$.\\ \textbf{\'Etape 4.}\\ Placer un point $O'$ sur $(d)$ entre $O$ et $P$ tel que $NO'=4,1$~cm. Tracer le cercle de centre $O'$ passant par $P$.\\ \textbf{\'Etape 5.}\\ En descendant de $3$~mm les centres toujours au-dessous de $O'$, tracer ainsi $14$ cercles toujours passant par $P$.\\ \textbf{\'Etape 6.}\\ Colorier la figure obtenue en alternant deux couleurs.\\ \end{multicols} \end{minipage} } \end{document}