Problem

Source: Stars O f Mathematics 2009 p3 - 1998 Moldova TST p11

Tags: lattice points, lattice, maximum, ratio, geometry



Let $A,B,C$ be nodes of the lattice $Z\times Z$ such that inside the triangle $ABC$ lies a unique node $P$ of the lattice. Denote $E = AP \cap BC$. Determine max $\frac{AP}{PE}$ , over all such configurations.