Smallest lattice triangles' circumcenter not lattice point
Source: Kürschák 2001, problem 3
July 13, 2014
geometrycircumcircleanalytic geometrygeometry unsolved
Problem Statement
In a square lattice let us take a lattice triangle that has the smallest area among all the lattice triangles similar to it. Prove that the circumcenter of this triangle is not a lattice point.