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Hi Peter,

Capturing the actual cursors proved to be elusive, so I drew what you will see.
Snap to grid=On.
When you draw a circle (Ellipse tool -L) and choose Radius creation the cursor is like the left image; just place the center of the crosshair on the grid mark and drag the circle. If you miss, no need to change tools from the Ellipse tool, just move crosshairs over the circle center (little x) and the cursor changes to the right image and it allows you to drag the circle back over a grid mark where it snaps.