Problem

Source: Romanian IMO Team Selection Test TST 1996, problem 15

Tags: function, geometry proposed, geometry



Let S be a set of n concentric circles in the plane. Prove that if a function f:SS satisfies the property d(f(A),f(B))d(A,B) for all A,BS, then d(f(A),f(B))=d(A,B), where d is the euclidean distance function.