Školjka

%V0 Show that in the plane there exists a convex polygon of 1992 sides satisfying the following conditions: (i) its side lengths are $1, 2, 3, \ldots, 1992$ in some order; (ii) the polygon is circumscribable about a circle. Alternative formulation: Does there exist a 1992-gon with side lengths $1, 2, 3, \ldots, 1992$ circumscribed about a circle? Answer the same question for a 1990-gon.