RO-NMO 2007 Problem 84

Let $ABCD$ be a tetrahedron.Prove that if a point $M$ in a space satisfies the relation: \begin{align*} MA^2 + MB^2 + CD^2 &= MB^2 + MC^2 + DA^2 &= MC^2 + MD^2 + AB^2 &= MD^2 + MA^2 + BC^2 . \end{align*} then it is found on the common perpendicular of the lines $AC$ and $BD$ .