MathDB
solid geometry

Source: Ukraine 1997 grade 11

July 22, 2009
geometrycircumcircleparallelogrammodular arithmetic3D geometryspheregeometry proposed

Problem Statement

On the edges AB,BC,CD,DA AB,BC,CD,DA of a parallelepiped ABCDA1B1C1D1 ABCDA_1 B_1 C_1 D_1 points K,L,M,N K,L,M,N are selected, respectively. Prove that the circumcenters of the tetrahedra A1AKN,B1BKL,C1CLM,D1DMN A_1 AKN, B_1 BKL, C_1 CLM, D_1 DMN are vertices of a parallelogram.
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