USAJMO 2026 Question 4

Triangle $ABC$ has circumcircle $\omega$ and circumcenter $O$. Lines $AO$ and $BC$ meet at $D$. Let $X$ be the $A$-excenter of triangle $ABD$, and $Y$ the $A$-excenter of triangle $ACD$. Prove that if $X\in\omega$, then $Y\in\omega$.

Proposed by Carl Schildkraut.

Manual essay; 1 editorial point, not official contest scoring.