The last known position is anywhere along the north and south corridors.
OK, the arcs define the possible location based on the SATCOM ping, but they are also limited by other factors based on maximum range based on fuel load and minimum airspeed range. We have a last known radar fix, and given the time this occurs we can calculate fuel burn to this point, so this defines the *start* of the following calculation. Next we can calculate the minimum airspeed possible from this point to reach the arc point and corresponding fuel burn - if the aircraft cannot have reached the arc then we know it was traveling at some higher speed (but I don't think that applies). Finally we can calculate the maximum range based on optimum cruise speed/min fuel burn, and plot that point on the arc. These two points define the segments of the corridors that apply. At any point between these limits we have a possible distance flown available based on fuel remaining.