In the tetrahedron ABCD, E and F are the midpoints of BC and AD, G is the midpoint of the segment EF. Construct a plane through G intersecting the segments AB, AC, AD in the points M,N,P respectively in such a way that the sum of the volumes of the tetrahedrons BMNP, CMNP and DMNP to be minimal.H. Lesov geometry3D geometrytetrahedroninequalitiesGeometric Inequalities