Why would you separate a circle into multiple arcs? Not just draw a full circle?
This comes from a problem of how the arc are defined in G-codes. In radius mode R, solving the path for a complete circle or semi-circle will cause severe numerical round-off problems that are unavoidable. This can lead to an error in the tool path. In fact, NIST guidelines state only use R mode for arc angles from 0- 165 and 195-345 degrees. Some CNC manufacturers actually don't allow users to draw a complete circle to avoid this problem altogether, limiting users to either a maximum 90 or 180 degree arc motions only. It is good practice to separate all of your arc motions into 90 or 180 degree motions. However, incremental arc mode I,J does not have this problem, but it's still good practice to separate your arcs.
Defining the Center Via the Radius Using "R"
We can also define the center just by specifying the radius of the circle. In this case, our circle has a radius of 2, so the g-code might be simply:
G02
X2Y0 R2
Many of you will be deciding right here and now that since R is easier to understand and shorter to write, you're just going to use R and forget about IJK. But, the CNC teachers in the world will suggest that you should prefer IJK. Their argument is that when you use IJK, you get a double check that your arc is correct.
Why?
Because the controller gets to compute an actual set of coordinates for the center via IJK. Once it has the center's coordinates, it can check that it is equa-distant from both end points. The check of each of those two distances is the double check. In the case of the "R" format, the controller has no such double check. It has to chose a center that guarantees equal distance.
Personally, I don't know if I agree with the CNC instructors that this is providing any extra checking or not. I say go with whichever approach makes sense for your particular situation, but you should definitely be familiar and comfortable with both. You're going to need to be comfortable with relative coordinates anyway, as they're darned handy. May as well get comfortable now.
It's kind of like being told you should only use the 4-jaw chuck on a lathe when you first start out so you'll get very comfortable dialing it in. It's a good skill to be good at as a machinist!