Given the three angles (A, B, C) of a spherical triangle, what's the radius (r) of the inscribed circle? My reference books are eager to tell me the radius of the circumcircle, or provide the inscribed radius if I know the three sides. Of course, one can get the sides from the angles, and do it that way. But Euclidean triangles have such a nice formula, area / r^2 = cot(A/2) + cot(B/2) + cot(C/2) you'd think there's a nice spherical formula, too. Anyway, I worked it out. For future reference: let u = sin^2 (A/2), v = sin^2 (B/2), w = sin^2 (C/2), p = uvw, q = uv+vw+wu, s = u+v+w -1 + 2s - s^2 + 4p Then sin^2 r = ------------------ 3 - 2s - s^2 + 4q That's satisfactorily symmetric, but still somewhat ugly. Is there a better formula? -- Don Reble djr@nk.ca