The points in the cellwhich do not belong tothe enlarged disc
The points in the celllying in a rhombus associated toa neighbouring cell.
The parts of the circumscribing disc notbelonging to one of these rhomboi.
The density of the distribution in the first type of region is of course 0, since by definition such a region contains no part of a disc. The density of the distribution in the third type is just the ratio of the radius of the disc to that of the larger one. Both densities are strictly less than the density of the disc in its regular circumscribed hexagon. The crux of the argument is now to examine regions of the second type.