{"status": "success", "data": {"description_md": "Let $A$, $B$, $C$, and $D$ be points in the coordinate plane on the hyperbola $\\tfrac{x^{2}}{20}-\\tfrac{y^{2}}{24}=1$ such that $ABCD$ is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than $BD^{2}$ for all such rhombi.\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\">A</span>, <span class=\"katex--inline\">B</span>, <span class=\"katex--inline\">C</span>, and <span class=\"katex--inline\">D</span> be points in the coordinate plane on the hyperbola <span class=\"katex--inline\">\\tfrac{x^{2}}{20}-\\tfrac{y^{2}}{24}=1</span> such that <span class=\"katex--inline\">ABCD</span> is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than <span class=\"katex--inline\">BD^{2}</span> for all such rhombi.</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": "2024 AIME I Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p10", "prev": "/problem/24_aime_I_p08"}}