{"status": "success", "data": {"description_md": "In rectangle $ABCD$, we have $AB=8$, $BC=9$, $H$ is on $BC$ with $BH=6$, $E$ is on $AD$ with $DE=4$, line $EC$ intersects line $AH$ at $G$, and $F$ is on line $AD$ with $GF \\perp AF$. Find the length of $GF$. \n\n<center>\n<img class=\"problem-image\" height=\"305\" src=\"https://latex.artofproblemsolving.com/d/f/e/dfe7f6dc99ad90df613e7fa1475792bedc4a9b8b.png\" width=\"248\"/>\n</center><br>\n\n$\\mathrm{(A) \\ } 16\\qquad \\mathrm{(B) \\ } 20\\qquad \\mathrm{(C) \\ } 24\\qquad \\mathrm{(D) \\ } 28\\qquad \\mathrm{(E) \\ } 30$", "description_html": "<p>In rectangle <span class=\"katex--inline\">ABCD</span>, we have <span class=\"katex--inline\">AB=8</span>, <span class=\"katex--inline\">BC=9</span>, <span class=\"katex--inline\">H</span> is on <span class=\"katex--inline\">BC</span> with <span class=\"katex--inline\">BH=6</span>, <span class=\"katex--inline\">E</span> is on <span class=\"katex--inline\">AD</span> with <span class=\"katex--inline\">DE=4</span>, line <span class=\"katex--inline\">EC</span> intersects line <span class=\"katex--inline\">AH</span> at <span class=\"katex--inline\">G</span>, and <span class=\"katex--inline\">F</span> is on line <span class=\"katex--inline\">AD</span> with <span class=\"katex--inline\">GF \\perp AF</span>. Find the length of <span class=\"katex--inline\">GF</span>.</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"305\" src=\"https://latex.artofproblemsolving.com/d/f/e/dfe7f6dc99ad90df613e7fa1475792bedc4a9b8b.png\" width=\"248\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } 16\\qquad \\mathrm{(B) \\ } 20\\qquad \\mathrm{(C) \\ } 24\\qquad \\mathrm{(D) \\ } 28\\qquad \\mathrm{(E) \\ } 30</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2003 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10A_p23", "prev": "/problem/03_amc10A_p21"}}