nonconvex quadrilaterals with fixed sum of distances
Source: VI All-Ukrainian Tournament of Young Mathematicians, Qualifying p1
May 25, 2021
geometryfixedconvexconvex quadrilateral3D geometryUkrainian TYM
Problem Statement
Find all nonconvex quadrilaterals in which the sum of the distances to the lines containing the sides is the same for any interior point. Try to generalize the result in the case of an arbitrary non-convex polygon, polyhedron.