{"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
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\n\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?


\\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}

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