{"status": "success", "data": {"description_md": "Triangle $ABC$ has side lengths $AB=120$, $BC=220$, and $AC=180$. Lines $\\ell_{A}$, $\\ell_{B}$, and $\\ell_{C}$ are drawn parallel to $\\overline{BC}$, $\\overline{AC}$, and $\\overline{AB}$, respectively, such that the intersection of $\\ell_{A}$, $\\ell_{B}$, and $\\ell_{C}$ with the interior of $\\triangle ABC$ are segments of length $55$, $45$, and $15$, respectively. Find the perimeter of the triangle whose sides lie on $\\ell_{A}$, $\\ell_{B}$, and $\\ell_{C}$.\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>Triangle <span class=\"katex--inline\">ABC</span> has side lengths <span class=\"katex--inline\">AB=120</span>, <span class=\"katex--inline\">BC=220</span>, and <span class=\"katex--inline\">AC=180</span>. Lines <span class=\"katex--inline\">\\ell_{A}</span>, <span class=\"katex--inline\">\\ell_{B}</span>, and <span class=\"katex--inline\">\\ell_{C}</span> are drawn parallel to <span class=\"katex--inline\">\\overline{BC}</span>, <span class=\"katex--inline\">\\overline{AC}</span>, and <span class=\"katex--inline\">\\overline{AB}</span>, respectively, such that the intersection of <span class=\"katex--inline\">\\ell_{A}</span>, <span class=\"katex--inline\">\\ell_{B}</span>, and <span class=\"katex--inline\">\\ell_{C}</span> with the interior of <span class=\"katex--inline\">\\triangle ABC</span> are segments of length <span class=\"katex--inline\">55</span>, <span class=\"katex--inline\">45</span>, and <span class=\"katex--inline\">15</span>, respectively. Find the perimeter of the triangle whose sides lie on <span class=\"katex--inline\">\\ell_{A}</span>, <span class=\"katex--inline\">\\ell_{B}</span>, and <span class=\"katex--inline\">\\ell_{C}</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": "2019 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p08", "prev": "/problem/19_aime_II_p06"}}