Question 70
Let $\omega$ be a semicircle with diameter $XY$. Let $M$ be the midpoint of $XY$. Let $A$ be an arbitrary point on $\omega$ such that $AX \lt AY$. Let $B$ and $C$ be points lying on the segments $XM$ and $YM$, respectively, such that $BM = CM$. The line through $C$ parallel to $AB$ intersects $\omega$ at $P$. The line through $B$ parallel to $AC$ intersects $\omega$ at $Q$. The line $PQ$ intersects the line $XY$ at a point $S$. Prove that the line $AS$ is tangent to $\omega$.