Determine the radius of a sphere that passes through the centroids of each face of a given tetrahedron inscribed in a unit sphere with center . Also, determine the distance from to the center of as a function of the edges of
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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
Školjka 
that passes through the centroids of each face of a given tetrahedron 
inscribed in a unit sphere with center 
. Also, determine the distance from 