Problems on Circles II: Halving a Set of Points

n

1

2

3

4

5

6

7

8

9

10

You are given

2n+3

points (

n≥1

) in the plane, no three on a line and no four on a circle. By using random points, this Demonstration shows that you can find a circle

C

passing through three of them (in red) such that, of the remaining

2n

points,

n

are in the interior (in yellow) and

n

are in the exterior (in blue) of

C

.