An alternative interpretation of the question: let's be lazy and compute the circles' pattern from the image.
Most of the triangles have area <200, and all the circles have area >200. I used
HighlightImage[img,ctds] to see this,
The thickness of the lines seems consistent, so adding 2 (about the thickness of the lines, in pixels) to each radius seems to work:
This is quick and dirty. In reality, intuition+Mathematica (as opposed to just asking Mathematica to numerically find centroids) is a more beautiful thing. I think it'd be pretty quick to bin the radii and centers along precise circles (they vary by ~.2 pixels due to anti-aliasing).