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ratio of volumes of tetrahedrons

Source: 1968 Polad Second Round p5

August 27, 2024
3D geometrygeometrytetrahedron

Problem Statement

The tetrahedrons ABCD ABCD and A1B1C1D1 A_1B_1C_1D_1 are situated so that the midpoints of the segments AA1 AA_1 , BB1 BB_1 , CC1 CC_1 , DD1 DD_1 are the centroids of the triangles BCDBCD, ACD ACD , ABD A B D and ABC ABC , respectively. What is the ratio of the volumes of these tetrahedrons?
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