{"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 $\\frac{HC}{JE}$.\n\n$\\text{(A)}\\ \\dfrac54 \\qquad \\text{(B)}\\ \\dfrac43 \\qquad \\text{(C)}\\ \\dfrac32 \\qquad \\text{(D)}\\ \\dfrac53 \\qquad \\text{(E)}\\ 2$", "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\">\\frac{HC}{JE}</span>.</p>&#10;<p><span class=\"katex--inline\">\\text{(A)}\\ \\dfrac54 \\qquad \\text{(B)}\\ \\dfrac43 \\qquad \\text{(C)}\\ \\dfrac32 \\qquad \\text{(D)}\\ \\dfrac53 \\qquad \\text{(E)}\\ 2</span></p>&#10;", "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"}}