Oh, ok.   I think you might be getting this result because you’re no longer on the circle.  The extent of the circle is from zero at the north pole, to 2V at its southernmost point, so the range of L is 0,2V.  This is because whatever the latitude of the southernmost point of the circle is, the midpoint of this latitude will be the latitude where we would find the circle center, if we were to dig deep enough.  I want to look into this further, but that might take a little while.   Here