Isogonal Conjugate

The isogonal conjugate of a point with respect to a triangle is constructed by reflecting each of the three lines from the point to a vertex across that vertex's angle bisector, and taking the common intersection point of the three reflected lines. Every point not lying on the triangle's sides or their extensions has a unique isogonal conjugate, and the construction is its own inverse, so the isogonal conjugate of the conjugate is the original point. Many notable triangle centers pair up as isogonal conjugates of each other, including the incenter, which is its own isogonal conjugate, and the pairing of the circumcenter with the orthocenter.