Sylvester-type theorems for unit circles Original Research Article

In this paper we study how can one generalize the well-known Sylvester theorem for congruent circles. We prove that for any finite set of at least two points in the plane which has diameter at most 2, there is a unit circle passing through exactly two points of the set. We conjecture that the same holds with the exception of one configuration in a more general case, when the diameter is at most two. In the later case, we show that there is a unit circle which contains at most 5 points.