IMO 1966 LL ROM38

Two concentric circles have radii R and r respectively. Determine

IMO 1966 LL ROM38

Origin: ROM

Problem

Two concentric circles have radii R and r respectively. Determine the greatest possible number of circles that are tangent to both these circles and mutually nonintersecting. Prove that this number lies between 2 \cdot \sqrt R+\sqrtr \sqrt R−\sqrtr −1 and 63 20 \cdot R+r R−r.