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(543) 4

Part of 1997 Tournament Of Towns

Problems(1)

support chord, convex polygon placed inside another convex polygon

Source: TOT 543 1997 Spring S A4 - Tournament Of Towns

9/11/2024
A convex polygon GG is placed inside a convex polygon F F so that their boundaries have no common points. A segment ss joining two points on the boundary of FF is called a support chord for GG if s contains a side or only a vertex of GG. Prove that (a) there exists a support chord for GG such that its midpoint lies on the boundary of GG, (b) there exist at least two such chords.
(P Pushkar)
geometryconvex polygon