CR-MO 2018 G2

Consider $\vartriangle ABC$ , with $AD$ bisecting $\angle BAC$ , $D$ on segment $BC$ . Let $E$ be a point on $BC$ , such that $BD = EC$ . Through $E$ we draw the line $\ell$ parallel to $AD$ and consider a point $P$ on it and inside the $\vartriangle ABC$ . Let $G$ be the point where line $BP$ cuts side $AC$ and let F be the point where line $CP$ to side $AB$ . Show that $BF = CG$ .