Given is a triangle $ABC$. Let $X$ be the reflection of $B$ in $AC$ and $Y$ is the reflection of $C$ in $AB$. The tangent to $(XAY)$ at $A$ meets $XY$ and $BC$ at $E, F$. Show that $AE=AF$.
Source: St. Petersburg 2023 9.7=11.6
Tags: geometry, geometric transformation, reflection
Given is a triangle $ABC$. Let $X$ be the reflection of $B$ in $AC$ and $Y$ is the reflection of $C$ in $AB$. The tangent to $(XAY)$ at $A$ meets $XY$ and $BC$ at $E, F$. Show that $AE=AF$.