The concept of isogonal conjugate points and isotomic conjugate points relative to a given triangle appears to have been introduced by Casey in 1888. Since then these topics have been treated in many important books, such as Johnson Coxeter and Greitzer and more recently Honsberger. The idea originated from the fact that the isogonal conjugates of the points on a fixed line form a circumconic of the triangle involved. That certain pairs of points are isogonal conjugates is of considerable theoretical significance. For example, that the symmedian point K in a triangle is the isogonal conjugate of its centroid G is an important result in understanding the significance of the symmedian point. The concepts involved, though well known to enthusiasts of triangle geometry, deserve additional publicity.