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

Home Analytic Geometry Triangle Incircle and Angle Bisectors
See also: Circumcircle of a Triangle, Excircle of a Triangle, Properties of a Right Triangle 
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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:
Home Analytic Geometry Triangle Incircle and Angle Bisectors

Last Update: 2010-12-06