Problem #PRU-87046

Problem

Let $M$ be the point of intersection of the medians of the triangle $A B C$ , and $O$ an arbitrary point on a plane. Prove that $O M^{2} = 1 / 3 (O A^{2} + O B^{2} + O C^{2}) - 1 / 9 (A B^{2} + B C^{2} + A C^{2}) .$

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