{"status": "success", "data": {"description_md": "Nondegenerate $\\triangle ABC$  has integer side lengths, ${\\overline{BD}}$ is an angle bisector, $AD = 3$, and $DC=8$. What is the smallest possible value of the perimeter?\n\n$\\textbf{(A)}\\ 30 \\qquad \\textbf{(B)}\\ 33 \\qquad \\textbf{(C)}\\ 35 \\qquad \\textbf{(D)}\\ 36 \\qquad \\textbf{(E)}\\ 37$", "description_html": "<p>Nondegenerate <span class=\"katex--inline\">\\triangle ABC</span>  has integer side lengths, <span class=\"katex--inline\">{\\overline{BD}}</span> is an angle bisector, <span class=\"katex--inline\">AD = 3</span>, and <span class=\"katex--inline\">DC=8</span>. What is the smallest possible value of the perimeter?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 30 \\qquad \\textbf{(B)}\\ 33 \\qquad \\textbf{(C)}\\ 35 \\qquad \\textbf{(D)}\\ 36 \\qquad \\textbf{(E)}\\ 37</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2010 AMC 10A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc10A_p17", "prev": "/problem/10_amc10A_p15"}}