RIOPLATENSE 2011 Problem 2

Let $ABC$ an acute triangle and $H$ its orthocenter. Let $E$ and $F$ be the intersection of lines $BH$ and $CH$ with $AC$ and $AB$ respectively, and let $D$ be the intersection of lines $EF$ and $BC$ . Let $\Gamma_1$ be the circumcircle of $AEF$ , and $\Gamma_2$ the circumcircle of $BHC$ . The line $AD$ intersects $\Gamma_1$ at point $I \neq A$ . Let $J$ be the feet of the internal bisector of $\angle{BHC}$ and $M$ the midpoint of the arc $\stackrel{\frown}{BC}$ from $\Gamma_2$ that contains the point $H$ . The line $MJ$ intersects $\Gamma_2$ at point $N \neq M$ . Show that the triangles $EIF$ and $CNB$ are similar.