Using RegionMember
:
SeedRandom[1];
pts = RandomReal[10, {10^5, 2}];
center = {5, 5};
radius = 2;
good = Select[pts, RegionMember[Disk[center, radius]]];
outside = Complement[pts, good];
ListPlot[{outside, good}
, AspectRatio -> Automatic
, PlotStyle -> {Directive[AbsolutePointSize[3]Directive[AbsolutePointSize[1], Red],
Directive[AbsolutePointSize[3]Directive[AbsolutePointSize[1], Darker@Green] }
, Epilog -> {Circle[center, radius]
}
]