Source : bissectrice.mp

input geometriesyr16;
input outilssyr;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
pair A,B,C,D[],E[];
A=u*(2,4);
B=u*(7,2.5);
C=u*(8,7);
D1=4/5[A,B];
D2=rotation(D1,A,angle(C-A)-angle(B-A));
trace demidroite(A,C);
trace demidroite(A,B);
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
path cc[],cd[];
cc1=coupdecompas(A,D1,10);
cc2=coupdecompas(A,D2,10);
cd1=coupdecompas(D1,symetrie(A,D1,D2),10);
cd2=coupdecompas(D2,symetrie(A,D1,D2),10);
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
trace demidroite(A,C);
trace demidroite(A,B);
trace compas(A,point(0) of cc1,1);
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
for k=1 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace compas(A,point(k*length cc1/3) of cc1,1);
  trace subpath(0,k*length cc1/3) of cc1;
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
path ce;
ce=arccercle(point(length cc1) of cc1,point(0) of cc2,A);
for k=1 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace compas(A,point(k*length ce/3) of ce,1);
  trace subpath(0,k*length ce/3) of ce withpen pencircle scaled0.5bp withcolor gris;
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
for k=1 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace ce withpen pencircle scaled0.5bp withcolor gris;
  trace compas(A,point(k*length cc2/3) of cc2,1);
  trace subpath(0,k*length cc2/3) of cc2;
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
trace demidroite(A,C);
trace demidroite(A,B);
trace cc1;
trace ce withpen pencircle scaled0.5bp withcolor gris;
trace cc2;
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
path cf,cg;
cf=arccercle(A,point(0) of cd2,D2);
cg=reverse(arccercle(point(0) of cd1,A,D1));
for k=0 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace ce withpen pencircle scaled0.5bp withcolor gris;
  trace cc2;
  trace compas(D2,point(k*length cf/3) of cf,1);
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
for k=1 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace ce withpen pencircle scaled0.5bp withcolor gris;
  trace cc2;
  trace compas(D2,point(k*length cd2/3) of cd2,1);
  trace subpath(0,k*length cd2/3) of cd2;
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
  for k=0 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace ce withpen pencircle scaled0.5bp withcolor gris;
  trace cc2;
  trace cd2;
  trace compas(D1,point(k*length cg/3) of cg,1);
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
for k=1 upto 3:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace demidroite(A,C);
  trace demidroite(A,B);
  trace cc1;
  trace ce withpen pencircle scaled0.5bp withcolor gris;
  trace cc2;
  trace cd2;
  trace compas(D1,point(k*length cd1/3) of cd1,1);
  trace subpath(0,k*length cd1/3) of cd1;
  nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
  fin;
endfor;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
trace demidroite(A,C);
trace demidroite(A,B);
trace cc1;
trace ce withpen pencircle scaled0.5bp withcolor gris;
trace cc2;
trace cd2;
trace cd1;
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
for k=0 upto 5:
  figure(0,0,11u,8u);
  trace feuillet withcolor blanc;
  trace regle(A,1.15[A,symetrie(A,D1,D2)],1);
  trace crayon(A,1.15[A,symetrie(A,D1,D2)],k/5,1);
  trace segment(A,(k/5)[A,1.15[A,symetrie(A,D1,D2)]]) withpen pencircle scaled 1.5bp withcolor orange;
trace demidroite(A,C);
trace demidroite(A,B);
trace cc1;
trace ce withpen pencircle scaled0.5bp withcolor gris;
trace cc2;
trace cd2;
trace cd1;
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
endfor;
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
trace demidroite(A,symetrie(A,D1,D2)) withpen pencircle scaled 1.5bp withcolor orange;
trace demidroite(A,C);
trace demidroite(A,B);
trace cc1;
trace ce withpen pencircle scaled0.5bp withcolor gris;
trace cc2;
trace cd2;
trace cd1;
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
for k=0 upto 2:
figure(0,0,11u,8u);
trace feuillet withcolor blanc;
trace demidroite(A,symetrie(A,D1,D2)) withpen pencircle scaled 1.5bp withcolor orange;
trace demidroite(A,C);
trace demidroite(A,B);
trace cc1;
trace ce withpen pencircle scaled0.5bp withcolor gris;
trace cc2;
trace cd2;
trace cd1;
trace appelation(A,symetrie(A,D1,D2),2mm,btex bissectrice de l'angle $\widehat{BAC}$ etex) withcolor rouge;
nomme.lft(A);
nomme.llft(B);
nomme.ulft(C);
trace marquedemidroite(B,A);
trace marquedemidroite(C,A);
fin;
endfor;
end