Ketinit();
Setparent(Cdyname()+"fig");
Setketcindyjs(["Nolabel=all"]);

Addax(0);
pA=Ptpos(A); pB=Ptpos(B); pC=Ptpos(C);
a=|pC-pB|; b=|pA-pC|; c=|pB-pA|;
Slider("S",[0,-6],[(a+b+c)/2,-6]);
s=2*Ptpos(S)_1;
if(s<c,
  t=s/c; p1=(1-t)*pA+t*pB;
,
  if(s<c+a,
    t=(s-c)/a; p1=(1-t)*pB+t*pC;
  ,
    t=(s-c-a)/b; p1=(1-t)*pC+t*pA;
  );
);
Pointdata("2",p1,["Size=3","Color=blue"]);
if(s<a,
  t=s/a; p2=(1-t)*pB+t*pC;
,
  if(s<a+b,
    t=(s-a)/b; p2=(1-t)*pC+t*pA;
  ,
    t=(s-a-b)/c; p2=(1-t)*pA+t*pB;
  );
);
Pointdata("3",p2,["Size=3","Color=green"]);
if(s<c,
  t=s/c; p3=(1-t)*pC+t*pA;
,
  if(s<b+c,
    t=(s-c)/b; p3=(1-t)*pA+t*pB;
  ,
    t=(s-b-c)/a; p3=(1-t)*pB+t*pC;
  );
);
Pointdata("4",p3,["Size=3","Color=red"]);
Listplot("2",[p1,p2,p3,p1],["Color=blue"]);
Listplot("1",[pA,pB,pC,pA],["dr,2"]);
a1=|pB-pC|; b1=|pC-pA|; c1=|pA-pB|;
s1=(a1+b1+c1)/2;
S1=sqrt(s1*(s1-a1)*(s1-b1)*(s1-c1));
a2=|p2-p3|; b2=|p3-p1|; c2=|p1-p2|;
s2=(a2+b2+c2)/2;
S2=sqrt(s2*(s2-a2)*(s2-b2)*(s2-c2));
Fontsize("L");
tmp="r=\frac{S_2}{S_1}="+Sprintf(S2/S1,3);
Expr([0,4],"e",tmp,["Size=2"]);
Fontsize("n");

Figpdf();
Windispg();