{"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>\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>\n<center>\n<img class=\"problem-image\" height=\"305\" src=\"https://latex.artofproblemsolving.com/d/f/e/dfe7f6dc99ad90df613e7fa1475792bedc4a9b8b.png\" width=\"248\"/>\n</center>\n<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>\n<hr><p>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": "2003 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10A_p23", "prev": "/problem/03_amc10A_p21"}}