The Spherical Incenter and Incircle.
In Euclidean geometry, the angel bisectors of a triangle are concurrent at the INCENTER, which is the center of the inscribed circle. In the sketch below, the same construction is carried out on a spherical triangle. Point Q is the incenter. The green circle is the incircle.
Drag points A, B, and C around slowly. The construction responds somewhat slowly...there are quite a few great and small circles constructed.