KöMaL 2010 B4316

Let $E$ denote the point closer to vertex $B$ that divides side $BC$ of a square ABCD in a 1:4 ratio. Let $F$ be the point obtained by reflecting about $C$ the point closer to $D$ that divides side $CD$ in a 1:2 ratio. Prove that the lines $AE$ and $BF$ intersect on the circumscribed circle of the square ABCD .