Well, some of them, anyway.
You can plot any azimuthal projection in polar coordinates, where the radius is a function of the angular distance from the center point.
So where two points' angular distances are the same, their radii are the same, and the projection of any locus of constant angular distance from the center point is a circle, if it appears at all.
Since you said that the tangent point is a pole, that means that parallels (lines of constant latitude) are those lines of constant angular distance. Ergo, Northern Hemisphere parallels appear as circles.
Since the Gnomonic projection can show only a single hemisphere, the Equator and parallels in the Southern hemisphere can't appear at all -- they would be an infinite distance from the center point.
The polar orientation of the projection even takes away complications resulting from the earth's not being a perfect sphere -- the radius formula changes a little, but the equal results from the same input remain.