There are other options. We use table saws at our shop. You can cut circles on a table saw....
You can also drive a nail with a rock. Merely because something is possible does not mean that it's reasonable.
Cutting circles, especially large circles with anything less than CNC tackle is problematic. Using hand and even stationary tools you're essentially trying to draw a circle freehand with a power tool. Good luck.
If you opt for a router, it will leave a nice clean edge but it can get away from you in an instant and ruin your workpiece.
If you choose a jigsaw it will leave a less than ideal edge but its easy to control.
It fairly easy to rig an extension table on a band saw which will give you a better and far more perpendicular edge but it's somewhat less forgiving that a jig saw in that if you should get off course it takes longer and more effort to get back on track.
If you go for the table saw like Primitive Pete above, most likely it's because that's all you have. You need more tools.