I am looking for a general approach for a type of problems as follows... Certain circumpolar star has a maximum azimuth A given for example as an angle from North to East and from North to West. Whats the declination of that star? The problem looks like this: draw a celestial sphere and add Pole and Zenith. Put some small circle around the Pole representing the path of the star. The Pole as the circle's center is on the local meridian (standard Zenith-North_pole-South_pole great circle). From Zenith to the horizon we draw any 90degree meridian that is touching the edge of the given circle around the Pole. Two such lines from Zenith to horizon are defining just how wide the circle around Pole is. How do I solve this? I took the place where meridians touch with the star path - where the star is in extreme position for measuring Azimuth; call that place X. The spherical triangle PZX has PZ=90-latitude and angle(pZx) is the Azimuth. However, beyond this the problem seems unsolvable. Using software to simulate numerical case, I get an equation of type cos x + sin x = ... which can be solved in a computer but I think thats no real solution.