Question 197
Let $A$ be a point lies outside circle $(O)$ and tangent lines $AB$, $AC$ of $(O)$. Consider points $D$, $E$, $M$ on $(O)$ such that $MD = ME$. The line $DE$ cuts $MB$, $MC$ at $R$, $S$. Take $X \in OB$, $Y \in OC$ such that $RX$, $RY \perp DE$. Prove that $XY \perp AM$.