Question 81
Let $ABC$ be a triangle with $AB \lt AC$. The bisector of $\angle BAC$ meets the side $BC$ at $D$. Let $k$ be the circle passing through $D$ that is tangent to the segments $AC$ and $AB$ at $E$ and $F$ respectively. Let $G$ be the second intersection point of $k$ with $BC$. Let $S$ be the intersection point of $EG$ and $DF$. Show that $AD$ is perpendicular to $BS$.