%%[slideshow] \input slideshow; author("Christophe Poulain & Régis Leclercq"); title("Construction de la médiatrice d'un segment"); %%[navigation] \input navigation; couleurboutons:=(1,1,0.3); couleurfond:=(0,0,0.7); %% Choix de LaTeX verbatimtex %&latex \documentclass[a4paper]{article} \usepackage[latin1]{inputenc} \usepackage[frenchb]{babel} \usepackage[dvips]{color,graphicx} \begin{document} etex %%[geometrie] input geometrie1 %%[Image] picture cp; cp=thelabel(btex \sf C.POULAIN \& R.LECLERCQ -- 2001 etex scaled 0.5,(0.85lawidth,0.03laheight)); footer(image(draw cp withcolor blue;)); %% -- navigation PDF & logos def navPDFlogos = init_navigation; navigation; internavigation; enddef; extra_endfig := extra_endfig & "navPDFlogos;"; % gs will need this prologues:=2; %fond d'écran noslides := 11; def doback = background := image(drawgradient((charcode/noslides)[white,white], (charcode/noslides)[white,white]);); enddef; doback; %cadre path cadre; cadre=(0.05lawidth,0.9laheight)--(0.95lawidth,0.9laheight)--(0.95lawidth,0.98laheight)--(0.05lawidth,0.98laheight)--cycle; draw cadre; %% -- instructions color C[]; C6=0.8white; vardef instruction(expr s) = fill cadre withcolor C6; label.rt(s,p100); enddef; %[Points] pair p[]; pair q[]; p0=(0.45lawidth,0.4laheight);%A p1=(0.70lawidth,0.5laheight);%B path ca,cb; ca=cercle(p0,abs(p1-p0)); cb=cercle(p1,abs(p1-p0)); p2=ca intersectionpoint cb;%I p3=syma(p2,p0,p1); numeric lca,lcb,lcaa,lcbb; lca=(angle(p2-p0))*(length ca)/360; lcaa=(length ca)+((angle(p3-p0))*(length ca)/360); lcb=(angle(p2-p1))*(length cb)/360; lcbb=(length cb)+((angle(p3-p1))*(length cb)/360); p100 = (0.07lawidth,0.94laheight); %[Animation] nextfig; % drawgradient(C0,C1); label(btex \large\bf Construction de etex scaled 2,(.502lawidth,.548laheight)) withcolor 0.3white; blabel(btex \large\bf Construction de etex scaled 2,(.50lawidth,.55laheight)); label(btex \large\bf la médiatrice d'un segment etex scaled 2,(.502lawidth,.448laheight)) withcolor 0.3white; blabel(btex \large\bf la médiatrice d'un segment etex scaled 2,(.5lawidth,.45laheight)); hyperdest("start"); endfig; discontinue; nextfig; instruction(btex 1. Trace un segment $[AB]$. etex); draw segment(p0,p1); label.llft(btex $A$ etex,p0); label.lrt(btex $B$ etex,p1); endfig; continue; nextfig; instruction(btex 2. Construis le cercle de centre $A$ et de rayon $AB$. etex); draw ca withcolor blue; endfig; continue; nextfig; instruction(btex 3. Construis le cercle de centre $B$ et de rayon AB. etex); draw ca; draw cb withcolor blue; endfig; nextfig; instruction(btex 4. Les cercles se coupent en deux points : $I$ et $J$. etex); draw cb withcolor white; draw ca withcolor white; draw (subpath(0,0.8*lca) of ca) dashed evenly scaled 2 withcolor green; draw (subpath(0.8*lca,1.2*lca) of ca) withcolor blue; draw (subpath(1.2*lca,0.95*lcaa) of ca) dashed evenly scaled 2 withcolor green; draw (subpath(0.95*lcaa,1.05*lcaa) of ca) withcolor blue; draw (subpath(1.05*lcaa,length ca) of ca) dashed evenly scaled 2 withcolor green; draw subpath(0,0.9*lcb) of cb dashed evenly scaled 2 withcolor green; draw subpath(0.9*lcb,1.1*lcb) of cb withcolor blue; draw subpath(1.1*lcb,0.95*lcbb) of cb dashed evenly scaled 2 withcolor green; draw subpath(0.95*lcbb,1.05*lcbb) of cb withcolor blue; draw subpath(1.05*lcbb,length cb) of cb dashed evenly withcolor green; labeloffset:=12pt; label.top(btex $I$ etex,p2); label.bot(btex $J$ etex,p3); labeloffset:=3bp; endfig; nextfig; instruction(btex 5. La droite $(IJ)$ est la médiatrice du segment $[AB]$. etex); draw (1.1[p3,p2]--1.1[p2,p3]) withcolor red; endfig; nextfig; draw codesegments(p0,milieu(p0,p1),milieu(p0,p1),p1,4); endfig; nextfig; draw codeperp(p2,milieu(p0,p1),p1); endfig; nextfig; discontinue; q0=(0.45lawidth,0.4laheight);%A q1=(0.60lawidth,0.3laheight);%B path da,db; da=cercle(q0,abs(q1-q0)); db=cercle(q1,abs(q1-q0)); q2=da intersectionpoint db;%I q3=syma(q2,q0,q1); lda=(angle(q2-q0))*(length da)/360; ldaa=(length da)+((angle(q3-q0))*(length da)/360); ldb=(angle(q2-q1))*(length db)/360; ldbb=(length db)+((angle(q3-q1))*(length db)/360); instruction(btex \underline{\color{blue} Récapitulatif} : On souhaite construire la médiatrice d'un segment $[AB]$. etex); draw segment(q0,q1); label.llft(btex $A$ etex,q0); label.lrt(btex $B$ etex,q1); endfig; nextfig; textcolour:=0.5green; blabel.rt(btex 1. Trace le cercle de centre $A$ et de rayon $AB$. etex, (0.05lawidth,0.85laheight)); %draw (0.05lawidth,0.85laheight)--(0.05lawidth,0.8laheight); %drawarrow (0.05lawidth,0.8laheight)--(0.1lawidth,0.8laheight); drawarrow (0.05lawidth,0.85laheight)..(0.075lawidth,0.8laheight)..(0.1lawidth,0.8laheight); draw (subpath(0.8*lda,1.2*lda) of da) withcolor blue; draw (subpath(0.95*ldaa,1.05*ldaa) of da) withcolor blue; endfig; nextfig; textcolour:=0.5blue; blabel.rt(btex 2. Trace le cercle de centre $B$ et de rayon $AB$. etex, (0.1lawidth,0.80laheight)); drawarrow (0.1lawidth,0.8laheight)..(0.1lawidth,0.75laheight)..(0.15lawidth,0.75laheight); draw (subpath(0.8*ldb,1.2*ldb) of db) withcolor blue; draw (subpath(0.95*ldbb,1.05*ldbb) of db) withcolor blue; endfig; nextfig; textcolour:=0.5[green,blue]; blabel.rt(btex 3. Les cercles se coupent en $I$ et $J$. etex, (0.15lawidth,0.75laheight)); labeloffset:=12pt; label.top(btex $I$ etex,q2); label.bot(btex $J$ etex,q3); labeloffset:=3bp; endfig; nextfig; textcolour:=red; pickup thin nib; drawarrow (0.1lawidth,0.7laheight)--(0.2lawidth,0.7laheight); blabel.rt(btex La droite $(IJ)$ est la médiatrice du segment $[AB]$. etex, (0.20lawidth,0.7laheight)); endfig; nextfig; draw 1.1[q3,q2]--1.1[q2,q3] withcolor red; draw codesegments(q0,milieu(q0,q1),milieu(q0,q1),q1,2); draw codeperp(q2,milieu(q0,q1),q1); endfig; end