The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Incircle and Angle Bisectors of a Triangle

The angle bisectors of a triangle are the lines which cut the inner angles of a triangle into equal halves. The angle bisectors are concurrent and intersect at the center of the incircle (incenter S).

Each side of a triangle is cut by the corresponding angle bisector into two segments whose lengths are related to the lengths of the adjacent sides:

The lengths of the angle bisectors are given by

The radius r of the incircle can be calculated from the area A of the triangle:

Last Update: 2010-12-06