Question

Why are the areas lying between the arctic circle and the north pole in the northern hemisphere and the antarctic circle and the south pole in the southern hemisphere very cold?

Answer 1

its a simple and direct answer.
in this regions the sun rays falls indirectly which results in a very low temperature.and also the oblique rays of the sun has to travel a longer distance during which the heat is lost in the upper layers of atmosphere...and so the region is cool.