Woops, I stand half-corrected. You CAN set segment count for the circle just drawn (after drawing), but there's a syntax to it - it's not "20" for a 20-segment circle, it's "20s" for a 20-segment circle. It has to be entered before you do anything else, though. So... to use it that way (it'll set the session segment count), you'd plant your centerpoint, establish your radius (dragging or typing), then type "36s" (for a 36-segment circle) into the "Measurements Toolbar" (the little box in the lower right) and press ENTER.
If you're drawing multiple circles without switching to another tool, you can't use the set-first method on subsequent circles. It only works for the first circle after switching to the circle tool. By that I mean... turn on the circle tool & type "3" to set the segment count to 3, then draw a circle (it'll have 3 segments). If you then type "10" with the intent of changing to a 10-segment circle, it won't do that right - instead it'll change the radius of your first (3-segment) circle to 10 units. You CAN use the post-facto technique, though, of drawing your second (or subsequent) circle's center & radius, then typing "10s" immediately thereafter.