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Putnam 1971 B4

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April 6, 2022
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Problem Statement

A "spherical ellipse" with foci A,BA,B on a given sphere is defined as the set of all points PP on the sphere such that PA⌢+PB⌢=\overset{\Large\frown}{PA}+\overset{\Large\frown}{PB}= constant. Here PA⌢\overset{\Large\frown}{PA} denotes the shortest distance on the sphere between PP and AA. Determine the entire class of real spherical ellipses which are circles.
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