Cones and Sphere Geometry Problem

Geometry Level 3

Three identical cones each have a radius of 50 and a height of 120. The cones are placed such that their circular bases touch one another. Then a sphere is placed such that it rests in the space created by the three cones, as shown.

If the top of the sphere is the same height as the top of the cones, what is the radius of the sphere to three decimal places?

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