MathDB

2

Part of 2002 Austrian-Polish Competition

Problems(1)

Diagonal of a convex polygon

Source: 2002 Austrian-Polish, problem 2

9/23/2006
Let P1P2…P2nP_{1}P_{2}\dots P_{2n} be a convex polygon with an even number of corners. Prove that there exists a diagonal PiPjP_{i}P_{j} which is not parallel to any side of the polygon.
geometryconvex polygonconvex