1999 IMO Problems/Problem 1

Problem

Determine all finite sets of at least three points in the plane which satisfy the following condition:

For any two distinct points and in , the perpendicular bisector of the line segment is an axis of symmetry of .

Solution

Upon reading this problem and drawing some points, one quickly realizes that the set

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.