I'm trying to find the point along a path at which I can see a given location at a fixed angle relative to my bearing. For example:

Imagine I'm flying in a plane from point A to point B and want to take a picture of something but my camera only looks straight out to the side. I can calculate the great circle between A and B, and if I calculate the bearing from the vector describing the great circle to the target and travel 90 degrees, I believe that would get the point I'm looking for, intersecting the great circle perpendicular to it.

But what if I can't look straight out the side? What if my "camera" is looking out at 80 degrees instead of 90 degrees relative to the direction of travel? If I choose a point on the great circle containing A and B I can find the bearing to B and the bearing to the target and just subtract. But is there a way to do it without iterating through points on the circle? I need a vector geometry wiz to make my Euclidean approximation more accurate.