{"year": "2021", "tier": "T2", "problem_label": "4", "problem_type": null, "exam": "Nordic_MO", "problem": "Let $A, B, C$ and $D$ be points on the circle $\\omega$ such that $A B C D$ is a convex quadrilateral. Suppose that $A B$ and $C D$ intersect at a point $E$ such that $A$ is between $B$ and $E$ and that $B D$ and $A C$ intersect at a point $F$. Let $X \\neq D$ be the point on $\\omega$ such that $D X$ and $E F$ are parallel. Let $Y$ be the reflection of $D$ through $E F$ and suppose that $Y$ is inside the circle $\\omega$.\n\nShow that $A, X$, and $Y$ are collinear.", "solution": "s", "metadata": {"resource_path": "Nordic_MO/segmented/en-2021-sol.jsonl", "problem_match": "\n\nProblem 4.", "solution_match": "\n## Solution"}}