Area of a spherical triangle bound by great circles is $$(\alpha + \beta + \gamma - \pi)r^2$$ Great circles are on the planes passing trough the center of the sphere. The question is about the area of a spherical triangle bound by small circles, that is circles which planes do not pass through the sphere's center.

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Problem illustration

The question is how to calculate area of the triangle with respect to $r$. This triangle can be described with great circles at particular $r$ but it is non-obvious how to relate great circle angles to small circle angles.


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