# Source : plaisir3fig10.mp

plaisir3fig10.mp
\input slideshow;
author("Christophe Poulain & Régis Leclercq");
title("Le Plaisir de la géométrie : fiche 310");
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}
\footnotesize
etex
%%[geometrie]
%input geometrie1
def orthocentre(expr p,q,r )=%(sommet-côté opposé)
begingroup
save $; pair$;
($-p) rotated 90=whatever*(r-q); ($-q) rotated 90=whatever*(p-r);
$endgroup enddef; def cercle(expr p,q)=%centre-rayon begingroup save$;
path $;$=fullcircle scaled (2*q) shifted p;
$endgroup enddef; def droite(expr a,b)=%Points begingroup save$;
path $;$=(-3)[a,b]--3[a,b];
$endgroup enddef; def codeang(expr p,q,r,n)=%point-sommet-point(sens direct)-rayon du codage begingroup save$,cc,b,c,f,seg,sege,d,e;
picture $;$=currentpicture;
path cc;%cercle pour le codage
cc=fullcircle scaled (2*n*unit) shifted q;
pair b,c,f;
path seg,sege;
seg=p--q;
sege=q--r;
b=cc intersectionpoint seg;
c=cc intersectionpoint sege;
numeric d,e;
d=(angle(b-q))*(length cc)/360;
e=(angle(c-q))*(length cc)/360;
draw subpath(d,e) of cc;
$endgroup enddef; vardef codeperp(expr a,b,c) = (b+5*unitvector(a-b))--(b+5*unitvector(a-b)+5*unitvector(c-b))--(b+5*unitvector(c-b)) enddef; def perp(expr p,q,r)=%point-droite begingroup save$,cc,ce,cd,cf;
picture $; pair cc,ce; path cd,cf;$=currentpicture;
cc=(r-q) rotated 90 shifted q;
ce=cc shifted (p-q);
cd=droite(cc shifted (p-q),q shifted (p-q));
draw cd dashed evenly withcolor blue;
cf=droite(q,r);
draw codeperp(ce,cf intersectionpoint cd,r);
$endgroup enddef; %%[Image] picture cp; cp=thelabel(btex \sf C.POULAIN \& R.LECLERQ -- 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; %Couleurs color aubergine,beige; aubergine = 3(37/256,2/256,29/256); beige = (0.77734375,0.67578125,0.4921875); C0 = (.5,1,1); C1 = (.9,.4,.5); C2 = 0.2[C0,C1]; C3 = 0.2[C1,C0]; C4 = 0.3[red,green]; C5=(.5,1,.25); %[Points] pair p[],h[],k[]; unit=1cm; p0=(0.5lawidth,0.5laheight);%O p1=(0.6lawidth,0.5laheight);%A for i:=2 upto 5 : p[i]=(p[i-1]-p0) rotated 72 shifted p0; endfor h1=orthocentre(p1,p2,p3); h2=orthocentre(p2,p3,p4); h3=orthocentre(p3,p4,p5); h4=orthocentre(p4,p5,p1); h5=orthocentre(p5,p1,p2); k1=droite(p1,p2) intersectionpoint droite(p3,p4); k2=droite(p2,p3) intersectionpoint droite(p4,p5); k3=droite(p3,p4) intersectionpoint droite(p5,p1); k4=droite(p4,p5) intersectionpoint droite(p1,p2); k5=droite(p5,p1) intersectionpoint droite(p2,p3); p100=(0.07lawidth,0.94laheight); %Animation nextfig; label(btex \Large\bf Le Plaisir de la Géométrie etex scaled 2,(.502lawidth,.548laheight)) withcolor 0.3white; blabel(btex \Large\bf Le Plaisir de la Géométrie etex scaled 2,(.50lawidth,.55laheight)); label(btex \Large\bf Fiche 310 etex scaled 2,(.502lawidth,.408laheight)) withcolor 0.3white; blabel(btex \Large\bf Fiche 310 etex scaled 2,(.5lawidth,.41laheight)); hyperdest("start"); endfig; discontinue; nextfig; instruction(btex 1. Trace un cercle de centre$O$et de rayon$OA=4,5\,cm$. etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); endfig; continue; nextfig; instruction(btex 2. Place sur le cercle, les points$B$,$C$,$D$et$E$tels que$\widehat{AOB}=\widehat{BOC}=\widehat{COD}=\widehat{DOE}=72$° etex); draw p1--p0--p2; draw codeang(p1,p0,p2,0.9); labeloffset:=8pt; label.urt(btex 72° etex,p0); labeloffset:=3bp; dotlabel.top(btex$B$etex,p2); endfig; nextfig; draw p0--p3; dotlabel.top(btex$C$etex,p3); endfig; nextfig; draw p0--p4; dotlabel.bot(btex$D$etex,p4); endfig; nextfig; draw p0--p5; dotlabel.bot(btex$E$etex,p5); endfig; discontinue; nextfig; instruction(btex 3. Construire les hauteurs du triangle$ABC$: elles se coupent en$H_1$etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); dotlabel.top(btex$B$etex,p2); dotlabel.top(btex$C$etex,p3); dotlabel.bot(btex$D$etex,p4); dotlabel.bot(btex$E$etex,p5); draw droite(p1,p2); draw droite(p1,p3); draw droite(p3,p2); draw perp(h1,p1,p2); endfig; nextfig; draw perp(h1,p2,p3); endfig; nextfig; draw perp(h1,p3,p1); dotlabel.top(btex$H_1$etex,h1); endfig; discontinue; nextfig; instruction(btex 4. Construis les hauteurs du triangle$BCD$: elles se coupent en$H_2$etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); dotlabel.top(btex$B$etex,p2); dotlabel.top(btex$C$etex,p3); dotlabel.bot(btex$D$etex,p4); dotlabel.bot(btex$E$etex,p5); dotlabel.top(btex$H_1$etex,h1); draw droite(p3,p2); draw droite(p4,p2); draw droite(p4,p3); draw perp(h2,p2,p3); draw perp(h2,p3,p4); draw perp(h2,p4,p2); dotlabel.top(btex$H_2$etex,h2); endfig; nextfig; instruction(btex 4.1. Les droites$(AB)$et$(CD)$se coupent en$K_1$. etex); draw droite(p1,p2) withcolor red; dotlabel.top(btex$K_1$etex,k1); endfig; discontinue; nextfig; instruction(btex 5. Construis les hauteurs du triangle$CDE$: elles se coupent en$H_3$etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); dotlabel.top(btex$B$etex,p2); dotlabel.top(btex$C$etex,p3); dotlabel.top(btex$D$etex,p4); dotlabel.bot(btex$E$etex,p5); dotlabel.bot(btex$H_1$etex,h1); dotlabel.top(btex$H_2$etex,h2); dotlabel.top(btex$K_1$etex,k1); draw droite(p3,p4); draw droite(p4,p5); draw droite(p5,p3); draw perp(h3,p3,p4); draw perp(h3,p4,p5); draw perp(h3,p5,p3); dotlabel.bot(btex$H_3$etex,h3); endfig; nextfig; instruction(btex 5.1. Les droites$(BC)$et$(DE)$se coupent en$K_2$. etex); draw droite(p3,p2) withcolor red; dotlabel.top(btex$K_2$etex,k2); endfig; discontinue; nextfig; instruction(btex 6. Construis les hauteurs du triangle$DEA$: elles se coupent en$H_4$etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); dotlabel.top(btex$B$etex,p2); dotlabel.top(btex$C$etex,p3); dotlabel.bot(btex$D$etex,p4); dotlabel.bot(btex$E$etex,p5); dotlabel.top(btex$H_1$etex,h1); dotlabel.top(btex$H_2$etex,h2); dotlabel.bot(btex$H_3$etex,h3); dotlabel.top(btex$K_1$etex,k1); dotlabel.top(btex$K_2$etex,k2); draw droite(p5,p4); draw droite(p1,p5); draw droite(p4,p1); draw perp(h4,p4,p5); draw perp(h4,p5,p1); draw perp(h4,p1,p4); dotlabel.bot(btex$H_4$etex,h4); endfig; nextfig; instruction(btex 6.1. Les droites$(CD)$et$(EA)$se coupent en$K_3$. etex); draw droite(p3,p4) withcolor red; dotlabel.lrt(btex$K_3$etex,k3); endfig; discontinue; nextfig; instruction(btex 7. Construis les hauteurs du triangle$EAB$: elles se coupent en$H_5$etex); draw cercle(p0,abs(p0-p1)) dashed evenly; dotlabel.ulft(btex$O$etex,p0); dotlabel.rt(btex$A$etex,p1); dotlabel.top(btex$B$etex,p2); dotlabel.top(btex$C$etex,p3); dotlabel.bot(btex$D$etex,p4); dotlabel.bot(btex$E$etex,p5); dotlabel.top(btex$H_1