{"status": "success", "data": {"description_md": "The coordinates of the vertices of isosceles trapezoid $ABCD$ are all integers, with $A=(20,100)$ and $D=(21,107).$ The trapezoid has no horizontal or vertical sides, and $\\overline{AB}$ and $\\overline{CD}$ are the only parallel sides. The sum of the absolute values of all possible slopes for $\\overline{AB}$ is $\\frac mn,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

The coordinates of the vertices of isosceles trapezoid ABCD are all integers, with A=(20,100) and D=(21,107). The trapezoid has no horizontal or vertical sides, and \\overline{AB} and \\overline{CD} are the only parallel sides. The sum of the absolute values of all possible slopes for \\overline{AB} is \\frac mn, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2000 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_II_p12", "prev": "/problem/00_aime_II_p10"}}