In this youtube at this point in time the designer snaps circles equidistantly around each other, but does not show what settings are necessary to achieve this?
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It's hard to see, and there's no commentary or explanation given in the video, but I think I know how it's done. No snapping options need to be set for it to work. In fact probably best to switch off all snapping in the snap controls bar so these don't conflict with rescaling.
In Edit > Preferences > Behavior > Transform, make sure the option to "Scale stroke widths" is unchecked.
Draw a circle, and stroke it, remove any fill if there is one.
Switch to the Select and Transform Objects tool F1
Duplicate it Ctrl+D
Hold down Shift+Alt* while clicking and dragging the transform handle until it snaps into position. This will constrain the scaling by the size of the object for each step. So if the object's bounding box is 50 units², the next steps will be 100, 150, 200, and so on.
Select the middle circle again
Repeat steps 4 to 6 until finished
*Note: If you are using a Mac, I assume the constrain shortcut will be Shift+Option instead. Perhaps a Mac user can confirm this.