{"status": "success", "data": {"description_md": "Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?\n\n$\\mathrm{(A)}\\ \\dfrac{1}{36}<br>\\qquad\\mathrm{(B)}\\ \\dfrac{1}{24}<br>\\qquad\\mathrm{(C)}\\ \\dfrac{1}{18}<br>\\qquad\\mathrm{(D)}\\ \\dfrac{1}{12}<br>\\qquad\\mathrm{(E)}\\ \\dfrac{1}{9}$\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 points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\dfrac{1}{36}\\qquad\\mathrm{(B)}\\ \\dfrac{1}{24}\\qquad\\mathrm{(C)}\\ \\dfrac{1}{18}\\qquad\\mathrm{(D)}\\ \\dfrac{1}{12}\\qquad\\mathrm{(E)}\\ \\dfrac{1}{9}</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": "2003 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/03_amc12B_p24"}}