295. Prove that six planes, each of which passes through the midpoint of one edge of a tetrahedron and is perpendicular to the opposite edge, intersect at one point (the Monge point).
This one wants a proof. Work it on paper, then read the official solution and mark
yourself. Be honest about it: the record is only any use to you if it is.
Official solution
295. Prove that all these planes pass through the point symmetric to the center of the sphere circumscribed around the tetrahedron with respect to its center of gravity.
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic, difficulty and ordering added
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