Y by Adventure10, junioragd, and 4 other users
Let
be a fixed positive integer. Given a set
of
points in the plane such that no three are collinear and no four concyclic, let
be the number of circles
that contain
in their interior, and let
Prove that there exists a positive integer
depending only on
such that the points of
are the vertices of a convex polygon if and only if 







![\[m(S)=a_1+a_2+\cdots + a_n.\]](http://latex.artofproblemsolving.com/4/9/b/49b928b1f20e2d1799a1234c7f25a2bc3d62d0dd.png)




This post has been edited 1 time. Last edited by djmathman, Oct 3, 2016, 3:25 AM
Reason: changed formatting to match imo compendium
Reason: changed formatting to match imo compendium