Ketinit();

Seteditable(0,["n=8","Size=18","Width=100"]);//no ketjs on
Setketcindyjs(["Label=[A,B]"]);
preL=[
 "<pf10/fp>Chain Circles",
 "<pf5>_;Move A to change the big circle, 
  and B to change the starting circle.<br>",
 "_;Change n to change the number of circles.</font></p>"
];
Ketcindyjsmain(preL);
Inspect(A,"ptsize",5.1);
Inspect(B,"ptsize",5.1);//no ketjs off

Addax("0");
//Setunitlen("22mm");

C.xy=0;
A.y=0;
A.x=max(A.x,0);

nstr="n=8";
//nstr=Textedit(0); //only ketjs
tmp=Strsplit(nstr,"=");
tmp=tmp_2;
if(length(tmp)>0,
 nall=parse(tmp);
);

rr(n):=(
  regional(tmp);
  tmp=R*(1+2*(tan(pi/n))^2);
  tmp-sqrt(tmp^2-(R^2-p^2));
);

R=|B-A|;
p=|C-A|;
//r=|D-C|;
r=rr(nall);
s=R+r+p;
a=(R+r-p)/s;
b=(R-r-p)/s;
c=(R-r+p)/s;
d=sqrt(a*(a-b)*(b+1));
h=sqrt(a*c/b);
th=arctan(b*h/d);
eps=10^(-5);

m0(pC,pA,pB):=(
 regional(cs);
 if(|pA-pC|<eps,
   cs=0;
 ,
   cs=Dotprod(pA-pC,pB-pC)/(|pA-pC|*|pB-pC|);
 );
 sqrt((1-cs)/(1+cs));
);

mk(m,k):=(
 if(|k*th-pi/2|>eps,
   h*(m+h*tan(k*th))/(-m*tan(k*th)+h);
 ,
   if(|m|<eps,
     if(m>0,m=eps,m=-eps);
   );
   h*h/(-m);
 );
);

rk(m):=(
 b*s*(m^2+h^2)/(2*(m^2+a));
//  s*(b*m^2+a*c)/(2*(m^2+a));
);

center(m):=(
 C+[a*s*(1-m^2)/(2*(m^2+a)),a*s*m/(m^2+a)];
);

Circledata("b",[A,R],["Msg=n"]);
Circledata("s",[C,r],["Msg=n"]);
m0=m0(C,A,B);
if(B.y<0,m0=-m0);
P0=center(m0);
r0=rk(m0);

//Pointdata("0",[P0],["Msg=n"]);
Circledata("0",[P0,r0],["Msg=n"]);

forall(1..(nall-1),
  m=mk(m0,#);
  r=rk(m);
  pP=center(m);
//  Pointdata(text(#),[pP],["Msg=n"]);
  Circledata(text(#),[pP,r],["Msg=n"]);
);

Windispg();
//Help("Ketcindyjsmain");