Let S be a set of n≥3 points in the interior of a circle.
a) Show that there are three distinct points a,b,c∈S and three distinct points A,B,C on the circle such that a is (strictly) closer to A than any other point in S, b is closer to B than any other point in S and c is closer to C than any other point in S.
b) Show that for no value of n can four such points in S (and corresponding points on the circle) be guaranteed. geometrycircumcirclecombinatorics proposedcombinatorics