{"status": "success", "data": {"description_md": "In $\\triangle ABC$ with integer side lengths,\n\n$$\\cos A=\\frac{11}{16}, \\qquad \\cos B= \\frac{7}{8}, \\qquad \\text{and} \\qquad\\cos C=-\\frac{1}{4}.$$<br>What is the least possible perimeter for $\\triangle ABC$?\n\n$\\textbf{(A) } 9 \\qquad \\textbf{(B) } 12 \\qquad \\textbf{(C) } 23 \\qquad \\textbf{(D) } 27 \\qquad \\textbf{(E) } 44$\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>In  <span class=\"katex--inline\">\\triangle ABC</span>  with integer side lengths,</p>&#10;<p> <span class=\"katex--display\">\\cos A=\\frac{11}{16}, \\qquad \\cos B= \\frac{7}{8}, \\qquad \\text{and} \\qquad\\cos C=-\\frac{1}{4}.</span> <br/>What is the least possible perimeter for  <span class=\"katex--inline\">\\triangle ABC</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 9 \\qquad \\textbf{(B) } 12 \\qquad \\textbf{(C) } 23 \\qquad \\textbf{(D) } 27 \\qquad \\textbf{(E) } 44</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": "2019 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p20", "prev": "/problem/19_amc12A_p18"}}