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Problem 1

Part of 1986 French Mathematical Olympiad

Problems(1)

midpoints of tetrahedron edges coplanar

Source: France 1986 P1

5/19/2021
Let ABCDABCD be a tetrahedron. (a) Prove that the midpoints of the edges AB,AC,BDAB,AC,BD, and CDCD lie in a plane. (b) Find the point in that plane, whose sum of distances from the lines ADAD and BCBC is minimal.
geometry3D geometrytetrahedroninequalities