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

78 Various Applications.
SECTION III.-CIRCUMCIRCLES.
75. To find the circumradius of a spherical triangle ABC.
Sol.-Bisect the arcs BC, CA at D, E, and let O be the intersection of perpendiculars to BC, CA, at D, E; then O is the
circumcentre.
A
Fig. 28.
DEM.-Join OA, OB, OC; then, equation (113), cos OB
= cos BD. cos OD, and cos OC = cos DC. cos OD. Hence OB
= OC. Similarly, OC = OA; therefore O is the circumcentre
of the triangle ABC. Again, the angle
OAB = OBA, OBC= OCB, and OCA = OA C;.-. OCB+A -=(A + C) =S;. OCB = S - A = 90~ - - E).
Let OC = R; then, from the triangle O CD we have, equation (109),
cos OCD = tan DC tan OC = tan a tan R;. tanR = tan a sin(A - E); (318)
and, substituting for tan a its value from equation (86), we
get
cot R= sin ( - E) in(B- ) sin(C- _) N
sin E sin E
(319)