\documentclass[11pt]{scrartcl}
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\begin{document}
\title{Mexico 2025/6}
\subtitle{Evan Chen}
\author{Twitch Solves ISL}
\date{Episode 170}
\maketitle

\section*{Problem}
Let $ABC$ be a triangle and let $I$ be the excenter opposite $A$.
The perpendicular line to $AI$
through $I$ intersects lines $AB$ and $AC$ at $E$ and $F$, respectively.
The circle $\omega_B$ is tangent to $EF$ and to $AB$ at $B$
such that it is outside triangle $AEF$.
Analogously, circle $\omega_C$ is tangent to $EF$ and to $AC$ at $C$
such that it is outside triangle $AEF$.
Line $IB$ cuts $\omega_B$ again at $X$ and line $IC$ cuts $\omega_C$ again at $Y$.

Let $\omega_A$ be the excircle of triangle $AEF$ opposite vertex $A$.
Show that the reflection of $\omega_A$ with respect to $EF$ is tangent to $XY$.



\section*{External Link}
\url{https://aops.com/community/p36502656}

\newpage

\section*{Solution}
TODO

\end{document}
