{"status": "success", "data": {"description_md": "Two points on the circumference of a circle of radius $r$ are selected independently and at random. From each point a chord of length $r$ is drawn in a clockwise direction. What is the probability that the two chords intersect?\n\n$\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{5}\\qquad\\textbf{(C)}\\ \\frac{1}{4}\\qquad\\textbf{(D)}\\ \\frac{1}{3}\\qquad\\textbf{(E)}\\ \\frac{1}{2}$", "description_html": "<p>Two points on the circumference of a circle of radius  <span class=\"katex--inline\">r</span>  are selected independently and at random. From each point a chord of length  <span class=\"katex--inline\">r</span>  is drawn in a clockwise direction. What is the probability that the two chords intersect?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{5}\\qquad\\textbf{(C)}\\ \\frac{1}{4}\\qquad\\textbf{(D)}\\ \\frac{1}{3}\\qquad\\textbf{(E)}\\ \\frac{1}{2}</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": "2011 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10A_p21", "prev": "/problem/11_amc10A_p19"}}