S>4Q in tetrahedron, Q is cross-sectional area
Source: Bulgaria 1980 P2
June 17, 2021
geometry3D geometrytetrahedron
Problem Statement
(a) Prove that the area of a given convex quadrilateral is at least twice the area of an arbitrary convex quadrilateral inscribed in it whose sides are parallel to the diagonals of the original one.
(b) A tetrahedron with surface area is intersected by a plane perpendicular to two opposite edges. If the area of the cross-section is , prove that .