This is a followup to the question
Area of triangle on a sphere (not spherical triangle)
Since it's now almost two years later, I'm making it a new question.
The problem is to find the area of pseudo spherical triangle. This is like a spherical triangle, but some of the edges are not an arc of a great circle.
This happens when intersecting spheres of different radii.
In the previous question, someone gave the general advice to try to integrate it. I tried with Mathematica, but cannot find a closed form. My guess is that there is no closed form in general.
Does anyone who has seen this problem know the answer? Does anyone know what this type of triangle is called?
Thanks.