Tetrahedron with two opposite sides equal.
Source: Vietnam MO 1983 P6
March 18, 2011
geometry3D geometrytetrahedronperimetergeometry unsolved
Problem Statement
Let be given a tetrahedron whose any two opposite edges are equal. A plane varies so that its intersection with the tetrahedron is a quadrilateral. Find the positions of the plane for which the perimeter of this quadrilateral is minimum, and find the locus of the centroid for those quadrilaterals with the minimum perimeter.