510

Part of 1989 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 510 All Soviet Union MO 1989 convex polygon area < \pi /4

Source:

A convex polygon is such that any segment dividing the polygon into two parts of equal area which has at least one end at a vertex has length

< 1

. Show that the area of the polygon is

< \pi /4

geometryconvex polygongeometric inequalityarea