OMM 2012 Problem 6

Consider an acute triangle $ABC$ with circumcircle $\mathcal{C}$ . Let $H$ be the orthocenter of $ABC$ and $M$ the midpoint of $BC$ . Lines $AH$ , $BH$ and $CH$ cut $\mathcal{C}$ again at points $D$ , $E$ , and $F$ respectively; line $MH$ cuts $\mathcal{C}$ at $J$ such that $H$ lies between $J$ and $M$ . Let $K$ and $L$ be the incenters of triangles $DEJ$ and $DFJ$ respectively. Prove $KL$ is parallel to $BC$ .