{"status": "success", "data": {"description_md": "Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?\n\n$\\textbf{(A) }\\frac{1}{6}\\qquad\\textbf{(B) }\\frac{1}{4}\\qquad\\textbf{(C) }\\frac{2-\\sqrt{2}}{2}\\qquad\\textbf{(D) }\\frac{1}{3}\\qquad\\textbf{(E) }\\frac{1}{2}\\qquad$", "description_html": "<p>Two concentric circles have radii  <span class=\"katex--inline\">1</span>  and  <span class=\"katex--inline\">2</span> . Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }\\frac{1}{6}\\qquad\\textbf{(B) }\\frac{1}{4}\\qquad\\textbf{(C) }\\frac{2-\\sqrt{2}}{2}\\qquad\\textbf{(D) }\\frac{1}{3}\\qquad\\textbf{(E) }\\frac{1}{2}\\qquad</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": "2014 AMC 10B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10B_p20", "prev": "/problem/14_amc10B_p18"}}