{"status": "success", "data": {"description_md": "Let $ABCD$ be a tetrahedron with $AB=41$, $AC=7$, $AD=18$, $BC=36$, $BD=27$, and $CD=13$, as shown in the figure. Let $d$ be the distance between the midpoints of edges $AB$ and $CD$. Find $d^{2}$.<br><br>$\\includegraphics[width=126, height=124, totalheight=124]{https://latex.artofproblemsolving.com/4/9/d/49d50e02f3f0268c768ed925016d1c4a0cf0b462.png}$\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>Let <span class=\"katex--inline\">ABCD</span> be a tetrahedron with <span class=\"katex--inline\">AB=41</span>, <span class=\"katex--inline\">AC=7</span>, <span class=\"katex--inline\">AD=18</span>, <span class=\"katex--inline\">BC=36</span>, <span class=\"katex--inline\">BD=27</span>, and <span class=\"katex--inline\">CD=13</span>, as shown in the figure. Let <span class=\"katex--inline\">d</span> be the distance between the midpoints of edges <span class=\"katex--inline\">AB</span> and <span class=\"katex--inline\">CD</span>. Find <span class=\"katex--inline\">d^{2}</span>.<br/><br/><img src=\"https://latex.artofproblemsolving.com/4/9/d/49d50e02f3f0268c768ed925016d1c4a0cf0b462.png\" width=\"126\" height=\"124\" class=\"problem-image\"/></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": 5, "problem_name": "1989 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p13", "prev": "/problem/89_aime_p11"}}