Two oints a and b lie on sphere of radius 12. The length of striaght line segment joining a and b is 12 root 3. What is the shortest path from a to b
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This is just a 2D problem in disguise. The shortest path is along a "great circle" - ie one with centre at the centre of the Earth. So in 2D the chord AB subtends angle 2C from the centre. We have
sinC = 6√3 / 12 = √3 / 2
C = 60 degrees
2C = 120 degrees
length of arc AB = (120/360) x 2pi x 12 = 8pi.
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