%%[slideshow] \input slideshow; author("Christophe Poulain & Régis Leclercq"); title("Construction de la bissectrice d'un angle"); %%[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,(0.95lawidth,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] unit=1cm; pair p[]; pair q[]; path cb,ci,cj; numeric lca,lcb,lcaa; p0=(0.3lawidth,0.40laheight);%B p1=(0.7lawidth,0.8laheight);%A p2=(0.6lawidth,0.3laheight);%C cb=cercle(p0,3cm); p3=(p0--p1) intersectionpoint cb;%I p4=(p0--p2) intersectionpoint cb;%J ci=cercle(p3,abs(p4-p3)); cj=cercle(p4,abs(p4-p3)); p5=cj intersectionpoint ci;%R lci=(angle(p3-p0))*(length cb)/360; lcj=(length cb)+(angle(p4-p0))*(length cb)/360; lcir=(length ci)+(angle(p5-p3))*(length ci)/360; lcjr=(angle(p5-p4))*(length cj)/360; p100=(0.07lawidth,0.94laheight); %[Animation] nextfig; 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 bissectrice d'un angle etex scaled 2,(.502lawidth,.408laheight)) withcolor 0.3white; blabel(btex \Large\bf la bissectrice d'un angle etex scaled 2,(.5lawidth,.41laheight)); hyperdest("start"); endfig; discontinue; nextfig; instruction(btex 1. Trace un angle $\widehat{ABC}$. etex); draw 1.1[p0,p1]--p0--1.1[p0,p2]; dotlabel.top(btex $A$ etex,p1); label.top(btex $B$ etex,p0); dotlabel.bot(btex $C$ etex,p2); endfig; continue; nextfig; instruction(btex 2. Trace un cercle $\cal C$ de centre $B$ (le sommet de l'angle) et de rayon quelconque. etex); draw (subpath(0,0.8lci) of cb) dashed evenly withcolor green; draw (subpath(0.8lci,1.2lci) of cb) withcolor blue; draw (subpath(1.2lci,0.95lcj) of cb) dashed evenly withcolor green; draw (subpath(0.95lcj,1.05lcj) of cb) withcolor blue; draw (subpath(1.05lcj,length cb) of cb) dashed evenly withcolor green; endfig; continue; nextfig; instruction(btex 3. Le cercle $\cal C$ coupe la demi-droite $[BA)$ en $I$. etex); dotlabel.top(btex $I$ etex,p3); endfig; nextfig; instruction(btex 4. Le cercle $\cal C$ coupe la demi-droite $[BC)$ en $J$. etex); labeloffset:=6pt; dotlabel.lrt(btex $J$ etex,p4); labeloffset:=3bp; endfig; nextfig; instruction(btex 5. Trace un cercle ${\cal C}_1$ de centre $I$ et de rayon $IJ$. etex); draw (subpath(0,0.8lci) of cb) dashed evenly withcolor white; draw (subpath(1.2lci,0.95lcj) of cb) dashed evenly withcolor white; draw (subpath(1.05lcj,length cb) of cb) dashed evenly withcolor white; draw (subpath(0,0.95lcir) of ci) dashed evenly withcolor green; draw (subpath(0.95lcir,1.05lcir) of ci) withcolor blue; draw (subpath(1.05lcir,length ci) of ci) dashed evenly withcolor green; endfig; nextfig; instruction(btex 6. Trace un cercle ${\cal C}_2$ de centre $J$ et de \underline{\bf même rayon} $IJ$. etex); draw (subpath(0,0.95lcir) of ci) dashed evenly withcolor white; draw (subpath(1.05lcir,length ci) of ci) dashed evenly withcolor white; draw (subpath(0,0.75lcjr) of cj) dashed evenly withcolor green; draw (subpath(0.75lcjr,1.25lcjr) of cj) withcolor blue; draw (subpath(1.25lcjr,length cj) of cj) dashed evenly withcolor green; endfig; nextfig; instruction(btex 6. Les cercles ${\cal C}_1$ et ${\cal C}_2$ se coupent en $R$. etex); draw (subpath(0,0.75lcjr) of cj) dashed evenly withcolor white; draw (subpath(1.25lcjr,length cj) of cj) dashed evenly withcolor white; labeloffset:=12pt; dotlabel.lrt(btex $R$ etex,p5); labeloffset:=3bp; endfig; nextfig; instruction(btex 7. La droite $(BR)$ est la bissectrice de l'angle $\widehat{ABC}$. etex); draw 2[p0,p5]--1.1[p5,p0] withcolor red; endfig; nextfig; draw codeang(p5,p0,p1,1); draw codeang(p5,p0,p2,1.5); endfig; nextfig; discontinue; instruction(btex \underline{Récapitulatif} : On souhaite construire la bissectrice d'un angle $\widehat{ABC}$. etex); q1=(0.2lawidth,0.3laheight);%A q0=(0.5lawidth,0.6laheight);%B q2=(0.65lawidth,0.45laheight);%C path cd; cd=cercle(q0,2cm); q3=(q0--q1) intersectionpoint cd;%I q4=(q0--q2) intersectionpoint cd;%J ldi=(length cd)+(angle(q3-q0))*(length cd)/360; ldj=(length cd)+(angle(q4-q0))*(length cd)/360; draw 1.1[q0,q1]--q0--1.1[q0,q2]; dotlabel.top(btex $A$ etex,q1); dotlabel.top(btex $C$ etex,q2); label.urt(btex $B$ etex,q0); endfig; nextfig; textcolour:=0.5green; blabel.rt(btex 1. Trace un cercle ${\cal C}$ de centre $B$ et de rayon quelconque. etex, (0.05lawidth,0.85laheight)); draw (subpath(0.85ldi,1.15ldi) of cd) withcolor blue; draw (subpath(0.95ldj,1.05ldj) of cd) withcolor blue; endfig; nextfig; textcolour:=0.5green; blabel.rt(btex Le cercle $\cal C$ coupe la demi-droite $[BA)$ en $I$ et la demi-droite $[BC)$ en $J$. etex,(0.075lawidth,0.82laheight)); dotlabel.top(btex $I$ etex,q3); dotlabel.top(btex $J$ etex,q4); endfig; nextfig; draw (0.05lawidth,0.85laheight)--(0.05lawidth,0.78laheight); drawarrow (0.05lawidth,0.78laheight)--(0.1lawidth,0.78laheight); endfig; nextfig; textcolour:=0.5blue; blabel.rt(btex 2. Trace le cercle de centre ${\cal C}_1$ de centre $I$ et de rayon $IJ$. etex, (0.1lawidth,0.78laheight)); path cdi,cdj; cdi=cercle(q3,abs(q3-q4)); cdj=cercle(q4,abs(q4-q3)); q6=cdj intersectionpoint cdi; q5=syma(q6,q3,q4); lcdi=(length cdi)+(angle(q5-q3))*(length cdi)/360; draw (subpath(0.9lcdi,1.1lcdi) of cdi) withcolor blue; endfig; nextfig; textcolour:=0.5blue; blabel.rt(btex Trace le cercle ${\cal C}_2$ de centre $J$ et de rayon $IJ$. etex,(0.125lawidth,0.75laheight)); lcdj=(length cdj)+(angle(q5-q4))*(length cdj)/360; draw (subpath(0.9lcdj,1.1lcdj) of cdj) withcolor blue; endfig; nextfig; textcolour:=0.5blue; blabel.rt(btex Les cercles ${\cal C}_1$ et ${\cal C}_2$ se coupent en $R$. etex,(0.125lawidth,0.72laheight)); labeloffset:=9pt; dotlabel.llft(btex $R$ etex,q5); labeloffset:=3bp; endfig; nextfig; textcolour:=red; drawarrow (0.05lawidth,0.68laheight)--(0.15lawidth,0.68laheight); blabel.rt(btex La droite $(BR)$ est la bissectrice de l'angle $\widehat{ABC}$. etex, (0.15lawidth,0.68laheight)); draw 1.8[q0,q5]--1.1[q5,q0] withcolor 0.75[blue,red]; draw codeang(q1,q0,q5,0.8);draw codeang(q1,q0,q5,0.85); draw codeang(q5,q0,q2,1);draw codeang(q5,q0,q2,1.05); endfig; end