How Much Shorter is the Straight Line?

Geometry Level 5

Consider a sphere of radius \(R=9\) centered on the origin \((x,y,z) = (0,0,0)\). Find the minimum path length from \((8,4,1)\) to \((-3,-6,-6)\), subject to the constraint that the path must not leave the sphere's surface.

Enter your answer as the ratio of this distance to the straight-line distance between the two points.

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