IMO Shortlist 1982 problem 6
Avg:
Avg:
Let be a square with sides length . Let be a path within which does not meet itself and which is composed of line segments with . Suppose that for every point on the boundary of there is a point of at a distance from no greater than . Prove that there are two points and of such that the distance between and is not greater than and the length of the part of which lies between and is not smaller than .
Izvor: Međunarodna matematička olimpijada, shortlist 1982