The sun gets closer to the arctic circle during the northern hemiplane summer. Withing the arctic circle, the sun is always close enough to be seen for at least one day per year.
In other words, when the sun is farthest from an observer and he is within the arctic circle, it is still close enough for him to observe it.
I can make you a diagram if you wish, but you search the wiki for seasons, you will find one that shows the sun's orbit during different seasons.