{"status": "success", "data": {"description_md": "Two particles move along the edges of equilateral $\\triangle ABC$ in the direction $$A\\Rightarrow B\\Rightarrow C\\Rightarrow A,$$ starting simultaneously and moving at the same speed. One starts at $A$, and the other starts at the midpoint of $\\overline{BC}$. The midpoint of the line segment joining the two particles traces out a path that encloses a region $R$. What is the ratio of the area of $R$ to the area of $\\triangle ABC$?\n\n$\\mathrm {(A)} \\frac{1}{16}\\qquad \\mathrm {(B)} \\frac{1}{12}\\qquad \\mathrm {(C)} \\frac{1}{9}\\qquad \\mathrm {(D)} \\frac{1}{6}\\qquad \\mathrm {(E)} \\frac{1}{4}$\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": "

Two particles move along the edges of equilateral \\triangle ABC in the direction A\\Rightarrow B\\Rightarrow C\\Rightarrow A, starting simultaneously and moving at the same speed. One starts at A , and the other starts at the midpoint of \\overline{BC} . The midpoint of the line segment joining the two particles traces out a path that encloses a region R . What is the ratio of the area of R to the area of \\triangle ABC ?

\\mathrm {(A)} \\frac{1}{16}\\qquad \\mathrm {(B)} \\frac{1}{12}\\qquad \\mathrm {(C)} \\frac{1}{9}\\qquad \\mathrm {(D)} \\frac{1}{6}\\qquad \\mathrm {(E)} \\frac{1}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2007 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p23", "prev": "/problem/07_amc12B_p21"}}