Question 41
Let $ABC$ be a triangle with circumcircle $\Gamma$ and circumcenter $O$. Denote by $M$ the midpoint of $BC$. Point $D$ is the reflection of $A$ over $BC$, and $E$ is the intersection of $\Gamma$ and ray $MD$. Let $S$ be the circumcenter of triangle $ADE$. Prove that $A, E, M, O$, and $S$ are concyclic.