NavList:

For visualizing something similar, I've found that it helps to remember that your horizon is somebody else's vertical circle, where your "degrees from north" is their "degrees from the horizon."  Your "circle of equal azimuth" is their "circle of equal altitude." 

Find "somebody else's position," determine where their zenith appears in your sky (traditional altitude and azimuth), and then you can use traditional methods to draw a circle of position centered about that point.

In this case, that "somebody else" is 90° away from you (we're going from horizontal to vertical, after all), so that "somebody else's zenith" is a point on your horizon and the resulting circule of position around that point will be a great circle.  From your target's azimuth, turn 90° left or right (doesn't matter as this is going to be a great circle), and then "somebody else's zenith" will be 5400 nmi (90°) in that direction.