Question 25
(HUN 6) Three disks of diameter $d$ are touching a sphere at their centers. Moreover, each disk touches the other two disks. How do we choose the radius $R$ of the sphere so that the axis of the whole figure makes an angle of $60^\circ$ with the line connecting the center of the sphere with the point on the disks that is at the largest distance from the axis? (The axis of the figure is the line having the property that rotation of the figure through $120^\circ$ about that line brings the figure to its initial position. The disks are all on one side of the plane, pass through the center of the sphere, and are orthogonal to the axes.)