See this earlier MO question. The union of n disks (represented in terms of its boundary arcs) can be constructed in $O(n\log n)$ time. So construct the union of the $n$ disks you are given, and separately construct the union of the $n+1$ disks including the one you want covered. The given disk is covered iff if and only if the two unions are the same.
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See this earlier MO question. The union of n disks (represented in terms of its boundary arcs) can be constructed in $O(n\log n)$ time. So construct the union of the $n$ disks you are given, separately construct the union of the $n+1$ disks including the one you want covered. The given disk is covered iff and only if the two unions are the same. |
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