{"status": "success", "data": {"description_md": "Three distinct segments are chosen at random among the segments whose end-points are the vertices of a regular $12$-gon. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?\n\n$\\textbf{(A)} \\ \\frac{553}{715} \\qquad \\textbf{(B)} \\ \\frac{443}{572} \\qquad \\textbf{(C)} \\ \\frac{111}{143} \\qquad \\textbf{(D)} \\ \\frac{81}{104} \\qquad \\textbf{(E)} \\ \\frac{223}{286}$\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>Three distinct segments are chosen at random among the segments whose end-points are the vertices of a regular  <span class=\"katex--inline\">12</span> -gon. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\ \\frac{553}{715} \\qquad \\textbf{(B)} \\ \\frac{443}{572} \\qquad \\textbf{(C)} \\ \\frac{111}{143} \\qquad \\textbf{(D)} \\ \\frac{81}{104} \\qquad \\textbf{(E)} \\ \\frac{223}{286}</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": 5, "problem_name": "2013 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p25", "prev": "/problem/13_amc12A_p23"}}