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
Congruent Isoscelizers Point
See also
Equal Parallelians Point, IsoscelizerExplore with Wolfram|Alpha
References
Kimberling, C. "Congruent Isoscelizers Point." http://faculty.evansville.edu/ck6/tcenters/recent/conisos.html.Referenced on Wolfram|Alpha
Congruent Isoscelizers PointCite this as:
Weisstein, Eric W. "Congruent Isoscelizers Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CongruentIsoscelizersPoint.html