A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

118 Small Circles on the Sphere.
original triangle and incircles of colunar triangles are (b - c), (c- a), (a - b).
Hence (see Art. 108) we have
23 = sin (b + c), 3 = sin (c+a), 12 = sin (a+b),
14 = sin (b + c), 24 = sin(c-a), 34 = sin (a +b).
Hence the condition (412) is fulfilled.
2. Prove that the mutual power of two cireles is equal to the mutual
power of two circles inverse to them.
3. If p, q, r be the normal co-ordinates of a point on the sphere, with
respect to the sides of a spherical triangle ABC; prove that they are connected by the relation
-1, cos C, cosB, p
cos C, -1, cos A, q
cos B, cos A, -1, r
p, q, r, -1
In the equation (414), Art. 110, let the triangle ABC be replaced by its
supplemental triangle, while the point D retains its position.
4. If a, b, c be the mutual distances of the spherical centres of three small
circles whose radii are rl, r2, r3; prove that if r be the radius of a circle
cutting them orthogonally,
4n2sec2r = 1, cos c, cos b, cos rL
cos c, c1, cos a co r
cos b, cos a, 1, cos rs
cos ri, cos r2, cos r3, 0