{"status": "success", "data": {"description_md": "Circles centered at $A$ and $B$ each have radius $2$, as shown. Point $O$ is the midpoint of $\\overline{AB}$, and $OA = 2\\sqrt {2}$. Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B$, respectively, and $EF$ is a common tangent. What is the area of the shaded region $ECODF$?\n$\n$\n
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$$\n$\\text{(A)}\\ \\frac {8\\sqrt {2}}{3} \\qquad \\text{(B)}\\ 8\\sqrt {2} - 4 - \\pi \\qquad \\text{(C)}\\ 4\\sqrt {2} \\qquad \\text{(D)}\\ 4\\sqrt {2} + \\frac {\\pi}{8} \\qquad \\text{(E)}\\ 8\\sqrt {2} - 2 - \\frac {\\pi}{2}$", "description_html": "

Circles centered at A and B each have radius 2 , as shown. Point O is the midpoint of \\overline{AB} , and OA = 2\\sqrt {2} . Segments OC and OD are tangent to the circles centered at A and B , respectively, and EF is a common tangent. What is the area of the shaded region ECODF ?
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$$\n$\\text{(A)}\\ \\frac {8\\sqrt {2}}{3} \\qquad \\text{(B)}\\ 8\\sqrt {2} - 4 - \\pi \\qquad \\text{(C)}\\ 4\\sqrt {2} \\qquad \\text{(D)}\\ 4\\sqrt {2} + \\frac {\\pi}{8} \\qquad \\text{(E)}\\ 8\\sqrt {2} - 2 - \\frac {\\pi}{2}$\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": "2007 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10A_p25", "prev": "/problem/07_amc10A_p23"}}