2013 ToT Spring Junior A p5, lattice triangle with 2 lattice points interior
Source:
March 4, 2020
geometrylattice pointsparallelcombinatorial geometry
Problem Statement
A point in the plane is called a node if both its coordinates are integers. Consider a triangle with vertices at nodes containing exactly two nodes inside. Prove that the straight line connecting these nodes either passes through a vertex or is parallel to a side of the triangle.