{"status": "success", "data": {"description_md": "Let $S$ be the set of sides and diagonals of a regular pentagon. A pair of elements of $S$ are selected at random without replacement. What is the probability that the two chosen segments have the same length?\n\n$\\textbf{(A) }\\frac{2}5\\qquad\\textbf{(B) }\\frac{4}9\\qquad\\textbf{(C) }\\frac{1}2\\qquad\\textbf{(D) }\\frac{5}9\\qquad\\textbf{(E) }\\frac{4}5$", "description_html": "<p>Let  <span class=\"katex--inline\">S</span>  be the set of sides and diagonals of a regular pentagon. A pair of elements of  <span class=\"katex--inline\">S</span>  are selected at random without replacement. What is the probability that the two chosen segments have the same length?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }\\frac{2}5\\qquad\\textbf{(B) }\\frac{4}9\\qquad\\textbf{(C) }\\frac{1}2\\qquad\\textbf{(D) }\\frac{5}9\\qquad\\textbf{(E) }\\frac{4}5</span> </p>\n<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": "2013 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10B_p13", "prev": "/problem/13_amc10B_p11"}}