3

Part of 2001 Kurschak Competition

Problems(1)

Smallest lattice triangles' circumcenter not lattice point

Source: Kürschák 2001, problem 3

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.

geometrycircumcircleanalytic geometrygeometry unsolved