Source : sommevecteurpara.mp

input geometriesyr16;
input outilssyr;
vues:=5;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
pair I,J,L;
I=(1u,3u);
J=(4u,6u);
L=(7u,2u);
drawarrow I--J;
drawarrow I--L;
label.lft(btex $I$ etex,I);
label.top(btex $L$ etex,J);
label.bot(btex $J$ etex,L);
fin;
for vue=0 upto vues:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
  draw compas(I shifted ((vue/vues)*(J-I)),L shifted ((vue/vues)*(J-I)),1);
fin;
endfor;
path cercless[];
cercless1=cercles(J,abs(L-I));
lJ=length cercless1+angle((L shifted(J-I) rotatedabout (J,-5))-J)*(length cercless1)/360;
lL=length cercless1+angle((L shifted(J-I) rotatedabout (J,5))-J)*(length cercless1)/360;
for vue=0 upto 2:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
  draw compas(J,(L shifted (J-I)) rotatedabout(J,-5+(vue/2)*10),1);
  draw subpath(lJ,lJ+(vue/2)*(lL-lJ)) of cercless1 withcolor blue;
  fin;
endfor
for vue=0 upto vues:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
  draw compas(I shifted ((vue/vues)*(L-I)),J shifted ((vue/vues)*(L-I)),1);
  draw subpath(lJ,lL) of cercless1 withcolor blue;
  fin;
endfor
cercless2=cercles(L,abs(J-I));
lp3=angle((J shifted(L-I) rotatedabout (L,-5))-L)*(length cercless2)/360;
lp4=angle((J shifted(L-I) rotatedabout (L,5))-L)*(length cercless2)/360;
for vue=0 upto 2:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
  draw compas(L,(J shifted (L-I)) rotatedabout(L,-5+(vue/2)*10),1);
  draw subpath(lJ,lL) of cercless1 withcolor blue;
  draw subpath(lp3,lp3+(vue/2)*(lp4-lp3)) of cercless2 withcolor blue;
  fin;
endfor
pair K;
K=cercless2 intersectionpoint cercless1;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
draw subpath(lJ,lL) of cercless1 withcolor blue;
draw subpath(lp3,lp4) of cercless2 withcolor blue;
draw J--K--L dashed evenly;
label.rt(btex $K$ etex,K);
fin;
for vue=0 upto vues:
  figure(0,0,11u,8u);
  draw regle(I,K,1);
  draw crayon(I,K,(vue/vues),1.5);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
  draw subpath(lJ,lL) of cercless1 withcolor blue;
  draw subpath(lp3,lp4) of cercless2 withcolor blue;
  draw J--K--L dashed evenly;
  label.rt(btex $K$ etex,K);
  draw I--(I+(vue/vues)*(K-I)) withpen pencircle scaled 1.5bp withcolor red;
  fin;
endfor
figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
draw subpath(lJ,lL) of cercless1 withcolor blue;
draw subpath(lp3,lp4) of cercless2 withcolor blue;
draw J--K--L dashed evenly;
label.rt(btex $K$ etex,K);
drawarrow I--K withpen pencircle scaled 1.5bp withcolor red;
trace appelation(I,K,2mm,btex $\overrightarrow{\strut IJ}+\overrightarrow{\strut IL}$ etex);
fin;
figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
draw subpath(lJ,lL) of cercless1 withcolor blue;
draw subpath(lp3,lp4) of cercless2 withcolor blue;
draw J--K--L dashed evenly;
label.rt(btex $K$ etex,K);
drawarrow I--K withpen pencircle scaled 1.5bp withcolor red;
trace appelation(I,K,2mm,btex $\overrightarrow{\strut IJ}+\overrightarrow{\strut IL}$ etex);
fin;
figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  drawarrow I--J;
  drawarrow I--L;
  label.lft(btex $I$ etex,I);
  label.top(btex $L$ etex,J);
  label.bot(btex $J$ etex,L);
draw subpath(lJ,lL) of cercless1 withcolor blue;
draw subpath(lp3,lp4) of cercless2 withcolor blue;
draw J--K--L dashed evenly;
label.rt(btex $K$ etex,K);
drawarrow I--K withpen pencircle scaled 1.5bp withcolor red;
trace appelation(I,K,2mm,btex $\overrightarrow{\strut IJ}+\overrightarrow{\strut IL}$ etex);
fin;
end
%On souhaite construire graphiquement la somme $\vecteur{IJ}+\vecteur{IL}$.
%Si on choisit le point $I$ pour origine de ce vecteur somme, on doit alors construire le point $K$ tel que $IJKL$ soit un parallélogramme.
%Le vecteur somme $\vecteur{IJ}+\vecteur{IL}$ est le vecteur $\vecteur{IK}$.