KöMaL 2014 B4673

$E$ is the intersection of the diagonals of a cyclic quadrilateral $ABCD$ , and $K$ is the centre of the circumscribed circle. The intersection of the lines of sides $AB$ and $CD$ is $F$ , and the intersection of the lines of sides $BC$ and $DA$ is $G$ . The second intersection of the circumscribed circles of triangles $BFC$ and $CGD$ is $H$ . Prove that the points $K$ , $E$ and $H$ are collinear.