Three Coplanar Bisectors in Unit Sphere Construction
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.
ABC
S
O=(0,0,0)
B'
B
S
a
b
c
a
b
c
supp
c