Question: Please do fast Problem 13. * Consider a tetrahedron. Join each vertex with the point of intersection of the medians of the opposite face. Prove

Please do fast

Problem 13. * Consider a tetrahedron. Join each vertex with the point of intersection of the medians of the opposite face. Prove that all 4 segments you constructed pass through one point O. Prove that the point O divides each segment in the proportion 1 : 3. Connect the midpoint of each edge of the tetrahedron to the midpoint of the opposite edge. Prove that the point O is the midpoint of each of three segments you just constructed

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