MathNet 2025-part-01 — 187 problems (EN–VI) Question 154

Let point $D$ lie on side $AB$ and point $E$ lie on side $BC$ of triangle $ABC$, such that quadrilateral $ADEC$ is cyclic. Let $X$, $Y$ be two distinct points on arc $DE$ of the circumcircle of triangle $BDE$, not containing $B$, such that $BX = BY$. Prove that line $XY$ is parallel to line $AC$.

(Khulan Tumenbayar)