Over there ---------------->
G2 and G3 are all you need for arcs, but you need to know the parameter requirements of your machine controller, just to be sure. Some controllers expect a new command every time the curve crosses a quadrant line (X or Y at 0, 90, 180, 270 degrees), or maybe every 180 degrees.
The other variable which you must determine, is whether the arc center coordinates must be in absolute values, or incremental values. This choice may be dependent on the current mode of your main program, G90 absolute or G91 incremental.
Having said that, the rest is a matter of correct mathematics.
You should be able to get ahold of some very inexpensive software to help you do all this much more quickly and accurately than you can with a calculator. Bobcad comes to mind, or if you are wanting more automated software that will help you with nesting profiles, together, Onecnc Profiler comes to mind.
If you want to talk math, just say so, and we'll launch into that
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)