{"status": "success", "data": {"description_md": "**Full credit goes to the staff team at Canada Math for authoring these problems.**\n\nLet $AB$ be a line segment. Let $C$ and $D$ be on the perpendicular from $A$ to $AB$, and $E$ be on the perpendicular from $B$ to $AB$ such that $BE=CD=2AC=2AB$ and $C$, $D$, $E$ are on the same side as $AB$. Let $AE$ and $BD$ intersect at $F$. If $\\sin^2(\\angle AFC)$ can be written as $\\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers, find $p+q$.", "description_html": "

Full credit goes to the staff team at Canada Math for authoring these problems.

Let AB be a line segment. Let C and D be on the perpendicular from A to AB, and E be on the perpendicular from B to AB such that BE=CD=2AC=2AB and C, D, E are on the same side as AB. Let AE and BD intersect at F. If \\sin^2(\\angle AFC) can be written as \\frac{p}{q} where p and q are relatively prime positive integers, find p+q.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Canada Math Contest #2 - Problem 8", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}