The incenter is the center of a circumference that can be circumscribed inside the triangle. That means that the distance from the circumcenter to the sides of the triangle is the same. In this case, it means that:
On the other hand, the segments from the circumcenter N to the vertices of the triangle are angle bisectors, and using that fact, it can be proven that the two triangles that form at each vertex from the angle bisectors are congruent. Then, we can also know that:
The congruence that cannot be deduced from the given information is:
