{"status": "success", "data": {"description_md": "A round table has radius $4$. Six rectangular place mats are placed on the table. Each place mat has width $1$ and length $x$ as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length $x$. Furthermore, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. What is $x$?\n\n
\n\n
\n\n$\\mathrm{(A)}\\ 2\\sqrt{5}-\\sqrt{3}\\qquad\\mathrm{(B)}\\ 3\\qquad\\mathrm{(C)}\\ \\frac{3\\sqrt{7}-\\sqrt{3}}{2}\\qquad\\mathrm{(D)}\\ 2\\sqrt{3}\\qquad\\mathrm{(E)}\\ \\frac{5+2\\sqrt{3}}{2}$", "description_html": "

A round table has radius 4 . Six rectangular place mats are placed on the table. Each place mat has width 1 and length x as shown. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length x . Furthermore, the mats are positioned so that the inner corners each touch an inner corner of an adjacent mat. What is x ?

\n
\n\n
\n

\\mathrm{(A)}\\ 2\\sqrt{5}-\\sqrt{3}\\qquad\\mathrm{(B)}\\ 3\\qquad\\mathrm{(C)}\\ \\frac{3\\sqrt{7}-\\sqrt{3}}{2}\\qquad\\mathrm{(D)}\\ 2\\sqrt{3}\\qquad\\mathrm{(E)}\\ \\frac{5+2\\sqrt{3}}{2}

\n

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": 4, "problem_name": "2008 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/08_amc10A_p24"}}