How do angle bisectors locate a triangle's incenter?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
geometry
This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).
In geometry, an angle bisector is a line segment originating from a triangle's vertex that divides the interior angle into two equal parts.1
The incenter is located at the unique point where all three of these angle bisectors intersect within the triangle. This point serves as the center of the triangle's incircle—the largest circle that can be drawn inside the triangle, which is tangent to all three of its sides.21