PAMO 2023 Problem 1

In a triangle $ABC$ with $AB<AC$ , $D$ is a point on segment $AC$ such that $BD = CD$ . A line parallel to $BD$ meets segment $BC$ at $E$ and line $AB$ at $F$ . Point $G$ is the intersection of $AE$ and $BD$ . Show that $\angle BCG = \angle BCF$ . (Côte d'Ivoire)