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midpoints of tetrahedron edges coplanar

Source: France 1986 P1

May 19, 2021
geometry3D geometrytetrahedroninequalities

Problem Statement

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.
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