Question 128
Let $ABC$ be a triangle. Let $D$ be a point on $AB$ and let $E$ be a point on $AC$ such that $BCED$ is cyclic. Let $F$ be the intersection of the segment $BE$ and the circumcircle of $ADC$ and let $G$ be the intersection of $CD$ and the circumcircle of $ABE$. Suppose that the segments $BG$ and $CF$ meets at $S$. Show that $\angle FAS = \angle GAS$.
(Proposed by Khulan Tumenbayar)
(Proposed by Khulan Tumenbayar)