Let $ABCD$ be a regular tetrahedron with center $O.$ Consider two points $M,N,$ such that $\overrightarrow{NO}=-3\overrightarrow{MO}.$ Prove or disprove that $$NA+NB+NC+ND\geq MA+MB+MC+MD$$
I tried to use CS in the Euclidean space $E_3$, but it does not help, because the minoration is too wide.
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