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 $RX, SY \perp DE$. Prove that $XY \perp AM$.
Problem
Source: 2021 Saudi Arabia Training Lists p6 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests
Tags: geometry, perpendicular, Tangents
