{"status": "success", "data": {"description_md": "Side $\\overline{AB}$ of $\\triangle ABC$ has length $10$. The bisector of angle $A$ meets $\\overline{BC}$ at $D$, and $CD = 3$. The set of all possible values of $AC$ is an open interval $(m,n)$. What is $m+n$?\n\n$\\textbf{(A) }16 \\qquad<br>\\textbf{(B) }17 \\qquad<br>\\textbf{(C) }18 \\qquad<br>\\textbf{(D) }19 \\qquad<br>\\textbf{(E) }20 \\qquad$\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>Side  <span class=\"katex--inline\">\\overline{AB}</span>  of  <span class=\"katex--inline\">\\triangle ABC</span>  has length  <span class=\"katex--inline\">10</span> . The bisector of angle  <span class=\"katex--inline\">A</span>  meets  <span class=\"katex--inline\">\\overline{BC}</span>  at  <span class=\"katex--inline\">D</span> , and  <span class=\"katex--inline\">CD = 3</span> . The set of all possible values of  <span class=\"katex--inline\">AC</span>  is an open interval  <span class=\"katex--inline\">(m,n)</span> . What is  <span class=\"katex--inline\">m+n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }16 \\qquad\\textbf{(B) }17 \\qquad\\textbf{(C) }18 \\qquad\\textbf{(D) }19 \\qquad\\textbf{(E) }20 \\qquad</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": "2018 AMC 12B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12B_p13", "prev": "/problem/18_amc12B_p11"}}