{"status": "success", "data": {"description_md": "Points $A,B,C,D,E$ and $F$ lie, in that order, on $\\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\\overline{GD}$, and point $J$ lies on $\\overline{GF}$. The line segments $\\overline{HC}, \\overline{JE},$ and $\\overline{AG}$ are parallel. Find $HC/JE$.\n\n$\\text{(A)}\\ 5/4 \\qquad \\text{(B)}\\ 4/3 \\qquad \\text{(C)}\\ 3/2 \\qquad \\text{(D)}\\ 5/3 \\qquad \\text{(E)}\\ 2$", "description_html": "<p>Points  <span class=\"katex--inline\">A,B,C,D,E</span>  and  <span class=\"katex--inline\">F</span>  lie, in that order, on  <span class=\"katex--inline\">\\overline{AF}</span> , dividing it into five segments, each of length 1. Point  <span class=\"katex--inline\">G</span>  is not on line  <span class=\"katex--inline\">AF</span> . Point  <span class=\"katex--inline\">H</span>  lies on  <span class=\"katex--inline\">\\overline{GD}</span> , and point  <span class=\"katex--inline\">J</span>  lies on  <span class=\"katex--inline\">\\overline{GF}</span> . The line segments  <span class=\"katex--inline\">\\overline{HC}, \\overline{JE},</span>  and  <span class=\"katex--inline\">\\overline{AG}</span>  are parallel. Find  <span class=\"katex--inline\">HC/JE</span> .</p>\n<p> <span class=\"katex--inline\">\\text{(A)}\\ 5/4 \\qquad \\text{(B)}\\ 4/3 \\qquad \\text{(C)}\\ 3/2 \\qquad \\text{(D)}\\ 5/3 \\qquad \\text{(E)}\\ 2</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": 3, "problem_name": "2002 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10A_p21", "prev": "/problem/02_amc10A_p19"}}