vinkelhalvererne

vinkelhalvererne are lines or rays that divide an angle into two equal angles. In geometry, each angle has a unique angle bisector. The angle bisector can be a line segment, a ray, or a line, depending on the context.

For a given angle AOB, its angle bisector is a ray OC such that the angle AOC is equal to the angle BOC. This implies that the measure of angle AOC is half the measure of angle AOB.

A common method to construct an angle bisector for an angle ABC uses a compass and straightedge. First, place the compass point at B and draw an arc that intersects both sides of the angle (BA and BC) at points D and E, respectively. Then, with the compass point at D, draw an arc in the interior of the angle. Repeat this step with the compass point at E, ensuring the compass width is the same or larger. The point where these two arcs intersect is F. The ray BF is the angle bisector of angle ABC.

In a triangle, the angle bisectors of the three interior angles are concurrent, meaning they all intersect at a single point. This point of concurrency is called the incenter of the triangle. The incenter is equidistant from the three sides of the triangle and is the center of the triangle's incircle, which is the largest circle that can be inscribed within the triangle.