I leave this as a simple exercise so that the reader can convert this solution from commandline to pgmagick (see below). The code underlying pgmagick is the same as the command line.
You can draw a circle larger and then "resize". This improves the distorted appearance of the circle by averaging the edge with the surrounding background during the resize operation.
Instead
gm convert -size 220x220 xc:none -fill white \ -draw "circle 110,110, 33.75,33.75" \ original.png
Do it:
gm convert -size 880x880 xc:none -fill white \ -draw "circle 440,440, 135,135" \ -resize 25% resized.png
You can try other sizes and decide which one is the smallest, for example,
gm convert -size 440x440 xc:none -fill white \ -draw "circle 220,220, 67.5,65.5" \ -resize 50% resized.png
This command line works with both GraphicsMagick ("gm convert") and ImageMagick ("convert")
Looking at the pgmagick documentation at http://pgmagick.readthedocs.org/en/latest/cookbook.html#scaling-a-image it is unclear what pgmagick suggests "resize". The documentation displays "img.scale", which is likely to result in a jagged circle. Using "-scale" in the above command line examples instead of "-resize" really creates the same jaggy image.
However, pgmagick allows you to specify the type of filter, as in
img.scale((150, 100), 'lanczos')
which should be equivalent to "-resize" and this is what you want.