MathNet 2023-part-04 — 191 problems (EN–VI) Question 165

Let $ABC$ be a triangle. A circle through $B$ and $C$ crosses the sides $AB$ and $AC$ at $P$ and $Q$, respectively. Points $X$ and $Y$ on segments $BQ$ and $CP$, respectively, satisfy $\angle ABY = \angle AXP$ and $\angle ACX = \angle AYQ$. Prove that $XY$ and $BC$ are parallel.
Andrei Chiriță