Let $M,N, P$ be the midpoints of the sides $BC,CA,AB$ of the triangle $ABC$, respectively, and let $G$ be the centroid of the triangle. Prove that if $BMGP$ is cyclic and $2BN = \sqrt3 AB$ , then triangle $ABC$ is equilateral.
Problem
Source: 2004 Romania JBMO TST 5.2 / BMO shortlist 2004
Tags: geometry, Equilateral, midpoints, cyclic quadrilateral, Centroid