Two circles A and B, both with radius 1, touch each other externally.
Four circles P,Q,R and S, all four with the same radius r, lie such that
P externally touches on A,B,Q and S,
Q externally touches on P,B and R,
R externally touches on A,B,Q and S,
S externally touches on P,A and R.
Calculate the length of r.[asy]
unitsize(0.3 cm);pair A, B, P, Q, R, S;
real r = (3 + sqrt(17))/2;A = (-1,0);
B = (1,0);
P = intersectionpoint(arc(A,r + 1,0,180), arc(B,r + 1,0,180));
R = -P;
Q = (r + 2,0);
S = (-r - 2,0);draw(Circle(A,1));
draw(Circle(B,1));
draw(Circle(P,r));
draw(Circle(Q,r));
draw(Circle(R,r));
draw(Circle(S,r));label("A", A);
label("B", B);
label("P", P);
label("Q", Q);
label("R", R);
label("S", S);
[/asy] tangent circlesradiusgeometry