In geometry, the congruent isoscelizers point is a special point associated with a plane triangle. It is a triangle center and it is listed as X(173) in Clark Kimberling's Encyclopedia of Triangle Centers. This point was introduced to the study of triangle geometry by Peter Yff in 1989.
An isoscelizer of an angle in a triangle is a line through points and , where lies on and on , such that the triangle is an isosceles triangle. An isoscelizer of angle is a line perpendicular to the bisector of angle .
Let be any triangle. Let be the isoscelizers of the angles respectively such that they all have the same length. Then, for a unique configuration, the three isoscelizers are concurrent. The point of concurrence is the congruent isoscelizers point of triangle .