Not sure I understand the problem correctly, but this is a pretty trivial application of pythagoras' theorem?
The radius is the hypothenuse in a rectangular triangle. A point is inside a circle with a given radius, if its distance from the center is equal or less than the radius. These two are pretty obvious.
The radius can thus be decomposed into an x and y coordinate where its length can be calculated according to pythagoras' formula. Or, more easily and computionally more efficient, its square can be calculated from the same formula without the square root. That's a common optimization.
Thus, for all points that are inside a circle, (dx*dx + dy*dy) <= r*r must be true (where dx is the point's x coordinate subtracted from the center). In the easiest unoptimized case, you just iterate over every single cell and check its midpoint coordinate accordingly. It's either true (inside) or false (not inside).
Further, a circle with a given diameter lies completely within a square whose sides are the length of the diameter. You can therefore optimize the search by only iterating over the cells that are in the (midpoint.x - x ... midpoint.x +x) and (midpoint.y -y ... midpoint.y+y) range.
So... in pseudo-C code, something like...
rr = radius*radius;
for(x = center.x - radius; x <= center.x + radius; ++x)
for(y = center.y - radius; y <= center.y + radius; ++y)
{
dx = center.x -x;
dy = center.y -y;
if((dx*dx + dy*dy) < rr)
point_inside(x, y);
}