In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. comm.). This point of concurrence is called the congruent isoscelizers point, and has triangle center function α = cos(1/2 B) + cos(1/2 C) - cos(1/2 A).

equal parallelians point | isoscelizer