Andrew VK3BFA wrote:
I want to turn up a round perspex piece to fit in a circular hole in
the front panel of a radio I am building. I start with a piece of
perspex 4 inches square, and turn in down to the required fit.

I did this to make some inspection hole covers for my neighbour's
homebuilt aircraft. BTW, Perspex = Lucite = Acrylic
Cut out approximately square piece of Perspex a little larger than the
required disk from sheet. Drill 4 holes near the corners.
Secure this to a square piece of wood (e.g. 3/4" ply) with four small
wood screws.
Mount in four jaw chuck.
Press firmly on the center with a live center. A bit of old inner tube
will prevent scratching.
Use a pointy, sharp bit to cut your circle at SLOW speed.

A few strokes with a file or abrasive paper will clean up the sharp edges.

Ted