Spheres snugly fitted into a cube

Geometry Level 5

A larger sphere A, having a radius R, is snugly fitted in a cube (i.e. sphere A touches all six faces of the cube). Further, a small sphere B is snugly fitted in the corner of cube (i.e. sphere B touches sphere A & three orthogonal faces meeting at the same vertex). Further, a smaller sphere C, having a radius r, is snugly fitted in the same corner of the cube (i.e. sphere C touches sphere B & three orthogonal faces meeting at the same vertex). Find out ratio of the radius R (of larger sphere A) to the radius r (of smaller sphere C)?

Details: None of the spheres touches any of 12 edges of the cube

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