{"status": "success", "data": {"description_md": "Squares $ABCD$ and $EFGH$ have a common center and $\\overline{AB}\\parallel \\overline{EF}$. The area of $ABCD$ is $2016$, and the area of $EFGH$ is a smaller positive integer. Square $IJKL$ is constructed so that each of its vertices lies on a side of $ABCD$ and each vertex of $EFGH$ lies on a side of $IJKL$. Find the difference between the largest and smallest possible integer values of the area of $IJKL$.\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": "<p>Squares <span class=\"katex--inline\">ABCD</span> and <span class=\"katex--inline\">EFGH</span> have a common center and <span class=\"katex--inline\">\\overline{AB}\\parallel \\overline{EF}</span>. The area of <span class=\"katex--inline\">ABCD</span> is <span class=\"katex--inline\">2016</span>, and the area of <span class=\"katex--inline\">EFGH</span> is a smaller positive integer. Square <span class=\"katex--inline\">IJKL</span> is constructed so that each of its vertices lies on a side of <span class=\"katex--inline\">ABCD</span> and each vertex of <span class=\"katex--inline\">EFGH</span> lies on a side of <span class=\"katex--inline\">IJKL</span>. Find the difference between the largest and smallest possible integer values of the area of <span class=\"katex--inline\">IJKL</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2016 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p08", "prev": "/problem/16_aime_II_p06"}}