MathDB

Let

S

be a set of

n\ge 3

points in the interior of a circle.

a)

Show that there are three distinct points

a,b,c\in 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.

Problem Statement