3 interior points in a grid based polygon Given a polygon with vertices on a grid with 3 interior grid points and no 3 vertices lying on the same line.
Is it true that all vertices are on the same circle?

EDITED
There is also another counter example with convex points:


Would this qualify as a counterexample (J - I - H - G - L  and then the red sides)? It is a polygon, it has vertices on a grid, 3 interior points, and no 3 vertices lying on the same line. 
