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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.
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Definition
An isoscelizer of an angle A in a triangle ABC is a line through points P1 and Q1, where P1 lies on AB and Q1 on AC, such that the triangle AP1Q1 is an isosceles triangle. An isoscelizer of angle A is a line perpendicular to the bisector of angle A.
Let ABC be any triangle. Let P1Q1, P2Q2, P3Q3 be the isoscelizers of the angles A, B, C respectively such that they all have the same length. Then, for a unique configuration, the three isoscelizers P1Q1, P2Q2, P3Q3 are concurrent. The point of concurrence is the congruent isoscelizers point of triangle ABC.