A 3D geometry problem

Geometry Level pending

Four small spheres each with radius 6 are each internally tangent to a large sphere with radius 17. The four small spheres form a ring with each of the four spheres externally tangent to its two neighboring small spheres. A sixth intermediately sized sphere is internally tangent to the large sphere and externally tangent to each of the four small spheres. Its radius is m n \frac {m}{n} , where m and n are relatively prime positive integers. Find m+n.

Source: Purple Comet Math Meet

The answer is 56.

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1 solution

Link: https://purplecomet.org/views/data/2020HSSolutions.pdf

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