{"status": "success", "data": {"description_md": "Three spheres with radii $11$, $13$, and $19$ are mutually externally tangent. A plane intersects the spheres in three congruent circles centered at $A$, $B$, and $C$, respectively, and the centers of the spheres all lie on the same side of this plane. Suppose that $AB^2 = 560$. Find $AC^2$.\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>Three spheres with radii <span class=\"katex--inline\">11</span>, <span class=\"katex--inline\">13</span>, and <span class=\"katex--inline\">19</span> are mutually externally tangent. A plane intersects the spheres in three congruent circles centered at <span class=\"katex--inline\">A</span>, <span class=\"katex--inline\">B</span>, and <span class=\"katex--inline\">C</span>, respectively, and the centers of the spheres all lie on the same side of this plane. Suppose that <span class=\"katex--inline\">AB^2 = 560</span>. Find <span class=\"katex--inline\">AC^2</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": 5, "problem_name": "2022 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_I_p11", "prev": "/problem/22_aime_I_p09"}}