I would like to know how to find a set of coordinates on a small circle some distance from another point. 
For example, lets say A = (39.73, -104.98) #Denver
B = (39.83, -106.06) #point approximately 50 nautical miles away from A along the great circle track to C
C = (40.75, -111.88) #Salt Lake City, approximately 323 nautical miles away from A
How do I get the set of orange coordinates when I don't know the angle but I do know the cross track distance?
For concreteness, lets say the outer points near B have a cross track distance of +- 30 nautical miles and the inner points have a cross track of +- 15nm.
And the points near C have a cross track of +- 25 nm.
Also I have an initial bearing from A to C of -1.34 #radians
Answer
If the unknown points are on the specified circles, and if you assume a simple circular reference surface (a sphere, not an ellipsoid), then it is easy to get the angle at A from AC to the unknown points:
angle = ctd / scd, where
ctd is your so-called cross-track distance (what I'd call arc distance), and
scd is your small-circle distance away from A
Then you "just" calculate the new coordinates of unknown point, U, say:
coordsU = traverse (coordsA, azimAC + angle, scd), where
coordsA are coordinates at A,
azimAC is azimuth AC, (conveniently, you already have this in radians),
angle and scd are as above,
traverse is the appropriate function for the so-called "direct" problem of spherical trigonometry -- for now, left as a separate exercise for you to research, or already available from some library.
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