MathDB

8

Part of 1992 IMO Shortlist

Problems(1)

1992-gon with side lengths 1, 2, 3, ..., 1992 circumscribed

Source: IMO Shortlist 1992, Problem 8

8/13/2008
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,…,1992 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,…,1992 1, 2, 3, \ldots, 1992 circumscribed about a circle? Answer the same question for a 1990-gon.
algebraconvex polygonincirclepolygonAdditive combinatoricsIMO Shortlist