{"status": "success", "data": {"description_md": "Consider the points $A(0,12)$, $B(10,9)$, $C(8,0)$, and $D(-4,7)$. There is a unique square $S$ such that each of the four points is on a different side of $S$. Let $K$ be the area of $S$. Find the remainder when $10K$ is divided by $1000$.\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>Consider the points <span class=\"katex--inline\">A(0,12)</span>, <span class=\"katex--inline\">B(10,9)</span>, <span class=\"katex--inline\">C(8,0)</span>, and <span class=\"katex--inline\">D(-4,7)</span>. There is a unique square <span class=\"katex--inline\">S</span> such that each of the four points is on a different side of <span class=\"katex--inline\">S</span>. Let <span class=\"katex--inline\">K</span> be the area of <span class=\"katex--inline\">S</span>. Find the remainder when <span class=\"katex--inline\">10K</span> is divided by <span class=\"katex--inline\">1000</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": 6, "problem_name": "2005 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_I_p15", "prev": "/problem/05_aime_I_p13"}}