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I would not do it this way because I have other options, but you could buy a circle jig from Rockler that cuts circles up to 52" or you can build one just like it
For something that thick I think I would cut a circle from 1/2 sheet stock, probably mdf, draw out the circle on your piece and cut it slightly large with a bandsaw or jigsaw and then put the mdf on the piece as a pattern and clean it up with a pattern bit. I'm sure someone will probably come in and tell you if this is a bad idea.
Actually, thinking about it, circle jig and plunge router, taking small bites would work fine.
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Jasper Jig works awesome. They have a plate (sold separately of course) you double stick to the top and the jig rides on that. Maybe copy it with the diameter you need?
http://www.amazon.com/Jasper-300J-Router...ords=jasper+jig
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Bandsaw to me seems like the best tool, although I have used the circle jig with a router when cutting an 8" circle of something this deep. Did need sanding, as light passes do leave score marks with each lowering of the bit.
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I rough cut arcs and circles with a good jigsaw ( go slow do not push the cut or it will twist the blade in the cut and cause tapered cuts; outward is ok inward is not Band saw is fine if you have enough support to hold up a heavy top just be aware that you can still over cut if not set properly
After that, I have a simple masonite jig router set up to make arcs or circles up to 48". I mount the router to the jig and a single pin set to the radius of the circle and cut it true.
The Jasper is fine but costs money. Mine is made from scrap and works exactly the same.... I just drill a small hole where I want the radius pin to set measuring from the inside of the cutter to the pin location, or if you want to just hook your tape on the bit add the diameter of the bit to the radius of the cut.
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Totally doable using a pivot point on the table saw. Jig saw it close and then go to the TS.