Angle bisector (GMT)

The angle bisector of an angle is the locus of points that are equidistant from the two sides of the angle. In triangle geometry, the angle bisector of a vertex divides the opposite side into segments proportional to the adjacent sides.

Important properties

• Every point on the angle bisector is equidistant from the sides of the angle.

• In a triangle, the three angle bisectors meet at a single point called the incenter.

• The incenter is the center of the circle inscribed in the triangle (incircle).

• The Angle Bisector Theorem: In triangle $ABC$, if the angle bisector of $A$ meets $BC$ at $D$, then $\frac{BD}{DC} = \frac{AB}{AC}$.