Final answer:
The name of the parallel of latitude 66 degrees 33 feet 38 inches North of the equator, within which there is at least one day of the year when there is no sunlight and one day a year when there is no sunset, is the Arctic Circle.
Step-by-step explanation:
The Arctic Circle is a line of latitude at 66.5 degrees north which marks the southernmost latitude where there is at least one day of the year with no sunlight and one day of the year with no sunset. This latitude is north of the equator, therefore the correct answer is option C) Arctic Circle.