VMO 1990 Problem 3
ABCD is a tetrahedron with volume V. We wish to make three plane cuts to give a parallelepiped three of whose faces and all of whose vertices belong to the surface of the tetrahedron. Find the intersection of the three planes if the volume of the parallelepiped is 11V/50. Can it be done so that the volume of the parallelepiped is 9V/40?
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