Question 140
Given $\triangle ABC$ where $AB \lt AC$, $M$ is the midpoint of $BC$. The circle $O$ passes through $A$ and is tangent to $BC$ at $B$, intersecting the lines $AM$, $AC$ at $D$, $E$ respectively. Let $CF \parallel BE$, intersecting $BD$ extended at $F$. Let the lines $BC$ and $EF$ intersect at $G$. Show that $AG = DG$.