Solved: In Exercises 8488, a great circle on a sphere S with center O and radius R is a
Chapter 12, Problem 85(choose chapter or problem)
In Exercises 8488, a great circle on a sphere S with center O and radius R is a circle obtained by intersecting S with a plane that passes through O (Figure 19). If P and Q are not antipodal (on opposite sides), there is a unique great circle through P and Q on S (intersect S with the plane through O, P, and Q). The geodesic distance from P to Q is defined as the length of the smaller of the two circular arcs of this great circle. Show that the geodesic distance from Q = (a, b, c) to the North Pole P = (0, 0, R) is equal to R cos1 c R .
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