Constructing the Incenter - Concept


The point of concurrency of the three angle bisectors of a triangle is the incenter. It is the center of the circle that can be inscribed in the triangle, making the incenter equidistant from the three sides of the triangle. To construct the incenter, first construct the three angle bisectors; the point where they all intersect is the incenter. The incenter is always located within the triangle.


One of the four special types of points of concurrency inside a triangle is the incenter. The incenter is the point of concurrency of the three angle bisectors. It is also the center of an inscribed circle.
So if we looked at this sketch right here we have a triangle and then we have a have a circle that's inscribed inside that triangle. So that means that this triangle is intersected by the circle only three times and that the center of that circle is therefore the same distance from the three sides.
So I could mark these three segments as being congruent and I'm measuring this along a perpendicular from that center of the circle to the side. So three key things about the incenter is that it's the angle bisectors that make it, it's the center of the inscribed circle which has the result of being equidistant from the sides of your triangle.

point of concurrency angle bisectors equidistant