palm router / trimmer

Drill a centre hole then use a mini router attached to an arm so that it describes a perfect circle. cut until there is about half an inch to go and finish the circle with hand tools.

That's how I would do it but, if the piece to be routed is stuck to a board with double sided tape, the centre circle will be fixed so can be cut all around. These Katsu palm routers are far cheaper than popular branded makes - Electric Wood Hand Trimmer Laminator 1/4" 3/8" 220V: Amazon.co.uk: DIY & Tools
 
like the inner centre circle and sticky tape
and i cant find a jigsaw in the uk with a rotating blade, only 45 degrees

Large routers usually have a hole in the base to fit an extended bar for circle cutting but the small ones such as this don't. Easy to get around, mount the router on a rectangle of fairly thin material (say 6mm ply) then bang a nail through at the pivot point, measured from the outside or inside of the cutter depending on whether you want the piece on the inside or outside of the circle. On thick material, do it in several cuts, going deeper each time. I have 4 routers but the light weight Katsu is used the most.
 
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