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Angle bisector
The angle bisector of a triangle divides the angle into two angles with equal measures.
Explanation
Each point of an angle bisector is equidistant from the sides of the angle. The incenter is the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, and is the center point of the inscribed circle of the triangle.
Angle bisectors and inscribed circle of a triangle
A bisector in a triangle divides the opposite side in the ratio of the adjacent sides.