m = 5; r = 3000;
    Table[pt[i] = RandomReal[{-2000,2000},2], {i, m}];
    circles = Table[Circle[pt[i], r], {i, m}];
    disks = circles /. Circle -> Disk;
    reg1 = RegionIntersection[disks];
    area1 = RegionMeasure[reg1];
    reg2 = RegionUnion[disks];
    area2 = RegionMeasure[reg2];
    g10 = Show[Graphics[{RandomColor[], #}& /@ circles, Axes-> True, 
               PlotRange->{{-5000, 5000}, {-5000, 5000}}],
          RegionPlot[reg1], PlotLabel->Row[{"ratio = ", area1 / area2}]]
![Mathematica graphics](https://i.sstatic.net/nsTDt.png)