IMO Shortlist 1985 problem 9


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2. travnja 2012.
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Determine the radius of a sphere S that passes through the centroids of each face of a given tetrahedron T inscribed in a unit sphere with center O. Also, determine the distance from O to the center of S as a function of the edges of T.
Izvor: Međunarodna matematička olimpijada, shortlist 1985