# 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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