{"status": "success", "data": {"description_md": "Line segment $\\overline{AB}$ is a diameter of a circle with $AB=24$. Point $C$, not equal to $A$ or $B$, lies on the circle. As point $C$ moves around the circle, the centroid (center of mass) of $\\triangle{ABC}$ traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?\n\n$\\textbf{(A) }25 \\qquad\n\\textbf{(B) }38 \\qquad\n\\textbf{(C) }50 \\qquad\n\\textbf{(D) }63 \\qquad\n\\textbf{(E) }75 \\qquad$", "description_html": "<p>Line segment  <span class=\"katex--inline\">\\overline{AB}</span>  is a diameter of a circle with  <span class=\"katex--inline\">AB=24</span> . Point  <span class=\"katex--inline\">C</span> , not equal to  <span class=\"katex--inline\">A</span>  or  <span class=\"katex--inline\">B</span> , lies on the circle. As point  <span class=\"katex--inline\">C</span>  moves around the circle, the centroid (center of mass) of  <span class=\"katex--inline\">\\triangle{ABC}</span>  traces out a closed curve missing two points. To the nearest positive integer, what is the area of the region bounded by this curve?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }25 \\qquad\n\\textbf{(B) }38 \\qquad\n\\textbf{(C) }50 \\qquad\n\\textbf{(D) }63 \\qquad\n\\textbf{(E) }75 \\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": "2018 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p13", "prev": "/problem/18_amc10B_p11"}}