if get('geometry2, 'version)=false then load("geometry2");
n:3;
/* Define points Ai=[xi,yi] */
for i:0 thru n-1 do
	A[i]:[concat(x,i),concat(y,i)];

/* Define circle centers Oi=[ui,vi] */
for i:0 thru n-1 do
	O[i]:[concat(u,i),concat(v,i)];

/* Define radii and angles */
for i:0 thru n-1 do (
	R[i]:concat(R,i),
	COS_P[i]:concat(Cos,i),
	SIN_P[i]:concat(Sin,i),
	l[i]:concat(l,i)
);

/* Ai is on the circle with center Oi and radius Ri */
eqns1:makelist(distance(O[i],A[i],R[i]),i,0,n-1);

/* Distance between Ai and A[i+1] is l[i] */
shift(k):=if k=n-1 then 0 else k+1;
lshift(k):=if k=0 then n-1 else k-1;
eqns2:makelist(distance(A[i],A[shift(i)],l[i]),i,0,n-1);

/* Pi is the angle between [Ai,Oi] and [A[i],A[i+1]] */
eqns3:apply(append,makelist(angle(cos_p[i],sin_p[i],O[i],A[i],A[shift(i)],
	r[i],l[i]),i,0,n-1));

/* Pi is the angle between [A[i-1],A[i]] and [Ai,Oi] */
eqns4:apply(append,makelist(angle(cos_p[i],sin_p[i],A[lshift(i)],A[i],O[i],
	l[lshift(i)],r[i]),i,0,n-1));

/* Combine all equations */
eqns:expand(append(eqns1,eqns2,eqns3,eqns4));

/* Introduce simplifications */
u0:0;
v0:0;
u1:1;
v1:0;

eqns:''eqns;
stringout("billiard1.out",eqns,listofvars(eqns));