MathDB

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]

Problem Statement