Yff center of congruence

In geometry, the Yff center of congruence is a special point associated with a triangle. This special point is a triangle center and Peter Yff initiated the study of this triangle center in 1987.[1]

Isoscelizer

An isoscelizer of an angle A in a triangle △ABC is a line through points P1, 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. Isoscelizers were invented by Peter Yff in 1963.[2]

Yff central triangle

Let △ABC be any triangle. Let P1Q1 be an isoscelizer of angle A, P2Q2 be an isoscelizer of angle B, and P3Q3 be an isoscelizer of angle C. Let △A'B'C' be the triangle formed by the three isoscelizers. The four triangles △A'P2Q3, △Q1B'P3, △P1Q2C', and △A'B'C' are always similar.

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