{"status": "success", "data": {"description_md": "A triangle has vertices $(0,0)$, $(1,1)$, and $(6m,0)$, and the line $y = mx$ divides the triangle into two triangles of equal area. What is the sum of all possible values of $m$?\n\n$\\textbf{(A)} - \\!\\frac {1}{3} \\qquad \\textbf{(B)} - \\!\\frac {1}{6} \\qquad \\textbf{(C)}\\ \\frac {1}{6} \\qquad \\textbf{(D)}\\ \\frac {1}{3} \\qquad \\textbf{(E)}\\ \\frac {1}{2}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A triangle has vertices  <span class=\"katex--inline\">(0,0)</span> ,  <span class=\"katex--inline\">(1,1)</span> , and  <span class=\"katex--inline\">(6m,0)</span> , and the line  <span class=\"katex--inline\">y = mx</span>  divides the triangle into two triangles of equal area. What is the sum of all possible values of  <span class=\"katex--inline\">m</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} - \\!\\frac {1}{3} \\qquad \\textbf{(B)} - \\!\\frac {1}{6} \\qquad \\textbf{(C)}\\ \\frac {1}{6} \\qquad \\textbf{(D)}\\ \\frac {1}{3} \\qquad \\textbf{(E)}\\ \\frac {1}{2}</span> </p>&#10;<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": "2009 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p15", "prev": "/problem/09_amc12A_p13"}}