# Area of spherical triangle bounded by small circles

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.

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.