{"status": "success", "data": {"description_md": "Let $ABC$ be a triangle with slides lengths $AB=6$, $BC=7$, and $CA=8$ with orthocenter $H$. Let $\\ell_A$, $\\ell_B$, $\\ell_C$ be lines going through $A$, $B$, $C$ on the outside of $\\triangle ABC$. Let $\\ell_A$, $\\ell_B$ intersect at $F$, $\\ell_B$ and $\\ell_C$ intersect at $D$, $\\ell_C$ and $\\ell_A$ intersect at $E$. Given that $\\triangle ABC\\stackrel{+}{\\sim} \\triangle DEF$ with $DH=11$. Find $EH^2+FH^2$.", "description_html": "<p>Let <span class=\"katex--inline\">ABC</span> be a triangle with slides lengths <span class=\"katex--inline\">AB=6</span>, <span class=\"katex--inline\">BC=7</span>, and <span class=\"katex--inline\">CA=8</span> with orthocenter <span class=\"katex--inline\">H</span>. Let <span class=\"katex--inline\">\\ell_A</span>, <span class=\"katex--inline\">\\ell_B</span>, <span class=\"katex--inline\">\\ell_C</span> be lines going through <span class=\"katex--inline\">A</span>, <span class=\"katex--inline\">B</span>, <span class=\"katex--inline\">C</span> on the outside of <span class=\"katex--inline\">\\triangle ABC</span>. Let <span class=\"katex--inline\">\\ell_A</span>, <span class=\"katex--inline\">\\ell_B</span> intersect at <span class=\"katex--inline\">F</span>, <span class=\"katex--inline\">\\ell_B</span> and <span class=\"katex--inline\">\\ell_C</span> intersect at <span class=\"katex--inline\">D</span>, <span class=\"katex--inline\">\\ell_C</span> and <span class=\"katex--inline\">\\ell_A</span> intersect at <span class=\"katex--inline\">E</span>. Given that <span class=\"katex--inline\">\\triangle ABC\\stackrel{+}{\\sim} \\triangle DEF</span> with <span class=\"katex--inline\">DH=11</span>. Find <span class=\"katex--inline\">EH^2+FH^2</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "Grinding Aces Math Exam 2025 - Problem 13", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}