MathDB
tetrahedrons, minimum sum of volumes

Source: Bulgaria 1973 P6

June 20, 2021
geometry3D geometrytetrahedroninequalitiesGeometric Inequalities

Problem Statement

In the tetrahedron ABCDABCD, EE and FF are the midpoints of BCBC and ADAD, GG is the midpoint of the segment EFEF. Construct a plane through GG intersecting the segments ABAB, ACAC, ADAD in the points M,N,PM,N,P respectively in such a way that the sum of the volumes of the tetrahedrons BMNPBMNP, CMNPCMNP and DMNPDMNP to be minimal.
H. Lesov