Construct the plane which minimizes the volume
Source: IMO LongList 1973 - P2
June 6, 2011
geometry3D geometrytetrahedrongeometry proposed
Problem Statement
Let and be three rays in the space, and a point "between these rays" (i. e. in the interior of the part of the space bordered by the angles and ). Consider a plane passing through and meeting the rays and in the points , respectively. There are infinitely many such planes; construct the one which minimizes the volume of the tetrahedron .