IMAC 2012 Problem 2

Circles $k_1,k_2$ intersect at $B,C$ such that $BC$ is diameter of $k_1$ .Tangent of $k_1$ at $C$ touches $k_2$ for the second time at $A$ .Line $AB$ intersects $k_1$ at $E$ different from $B$ , and line $CE$ intersects $k_2$ at F different from $C$ . An arbitrary line through $E$ intersects segment $AF$ at $H$ and $k_1$ for the second time at $G$ .If $BG$ and $AC$ intersect at $D$ , prove $CH//DF$ .