{"status": "success", "data": {"description_md": "Triangle $ABC$ has side-lengths $AB = 12, BC = 24,$ and $AC = 18.$ The line through the incenter of $\\triangle ABC$ parallel to $\\overline{BC}$ intersects $\\overline{AB}$ at $M$ and $\\overline{AC}$ at $N.$ What is the perimeter of $\\triangle AMN?$\n\n$\\textbf{(A)}\\ 27 \\qquad<br>\\textbf{(B)}\\ 30 \\qquad<br>\\textbf{(C)}\\  33 \\qquad<br>\\textbf{(D)}\\ 36 \\qquad<br>\\textbf{(E)}\\ 42$\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>Triangle  <span class=\"katex--inline\">ABC</span>  has side-lengths  <span class=\"katex--inline\">AB = 12, BC = 24,</span>  and  <span class=\"katex--inline\">AC = 18.</span>  The line through the incenter of  <span class=\"katex--inline\">\\triangle ABC</span>  parallel to  <span class=\"katex--inline\">\\overline{BC}</span>  intersects  <span class=\"katex--inline\">\\overline{AB}</span>  at  <span class=\"katex--inline\">M</span>  and  <span class=\"katex--inline\">\\overline{AC}</span>  at  <span class=\"katex--inline\">N.</span>  What is the perimeter of  <span class=\"katex--inline\">\\triangle AMN?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 27 \\qquad\\textbf{(B)}\\ 30 \\qquad\\textbf{(C)}\\  33 \\qquad\\textbf{(D)}\\ 36 \\qquad\\textbf{(E)}\\ 42</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": "2011 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p14", "prev": "/problem/11_amc12A_p12"}}