Three Coplanar Bisectors in Unit Sphere Construction
Draw a spherical triangle on the surface of the unit sphere centered at . Let be the point opposite on . Let the sides opposite the corresponding vertices be the arcs , , . Then the bisectors of , and (the supplementary angle of ) lie in the same plane.
Vectors parallel to the bisectors of , , are , , , but , so the vectors are coplanar [3, p. 83].
 Wikipedia. "Spherical Law of Cosines." (May 15, 2017) en.wikipedia.org/wiki/Spherical_law_of _cosines.
 Wikipedia. "Spherical Trigonometry." (May 15, 2017) en.wikipedia.org/wiki/Spherical_trigonometry.
 V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.