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
%V0
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 $T.$
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