# Area of of spherical triangle with curved sides

The area of a spherical triangle (sphere radius $a$ ) is given by spherical deficit $(A+B+C-\pi)$ times $a^2$ when enclosed between great circular arcs.

If tangential curvature radii are $Rg_a, Rg_b, Rg_c$ what is the area of the spherical triangle enclosed between small circles? Positive if apex angle reduces with respect to a geodesic.

• If I intersect a sphere with a plane (not through the origin!) then the result is a circle of some radius $R$ lying on the sphere. Is this $R$ what is meant by 'tangential curvature radii'? – Semiclassical Sep 9 '16 at 17:11
• Yes, tangential radius of curvature $Rg$. Changed sphere radius symbol to $a$ to remove the ambiguity. – Narasimham Sep 9 '16 at 17:26