JBMO-SL 2002 Problem 8

Let $ABC$ be a triangle with centroid $G$ and $A_1,B_1,C_1$ midpoints of the sides $BC,CA,AB$ . A paralel through $A_1$ to $BB_1$ intersects $B_1C_1$ at $F$ . Prove that triangles $ABC$ and $FA_1A$ are similar if and only if quadrilateral $AB_1GC_1$ is cyclic.