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volumes of tetrahedra, midpoints of medians related

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1999 p2

February 20, 2020
3D geometrytetrahedronVolumegeometry

Problem Statement

In a tetrahedron ABCD,EABCD, E and FF are the midpoints of the medians from AA and DD. Find the ratio of the volumes of tetrahedra BCEFBCEF and ABCDABCD.
Note: Median in a tetrahedron connects a vertex and the centroid of the opposite side.
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