Hyperbolic
Incenter
The incenter of a triangle is the intersection point
of the three angle bisectors.
The incenter of a hyperbolic
triangle
always exists, that is, the three inner bisectors always intersect and,
moreover, the intersection point is inside the triangle.
The incenter
equidists from the three sides (not of the vertices) of the hyperbolic
triangle. It is because, in general, given two rays that determine an
angle, each point of the angle bisector equidist from the rays. From
the incenter
we can construct the incircle
for the triangle.
To construct the incenter it is only
necessary to fix the triangle, to draw the hyperbolic
angle
bisectors in two of the
vertices of the triangle and to consider its intersection.
Triangles
Hyperbolic
geometry
