Yff center of congruence

In geometry, the Yff center of congruence is a special point associated with a triangle.

In this special case △A'B'C' formed by the three isoscelizers is called the Yff central triangle of △ABC.

The point to which △A'B'C' reduces to is called the Yff center of congruence of △ABC.

The geometrical construction for locating the Yff center of congruence has an interesting generalization.

The generalization asserts that the lines AD, BE, CF are concurrent.

Reference triangle △ ABC
△ A'P 2 Q 3 ≅ △ Q 1 B'P 3 ≅ △ P 1 Q 2 C' ≅
△ A'B'C' ( Yff central triangle )
Animation showing the continuous shrinking of the Yff central triangle to the Yff center of congruence. The animation also shows the continuous expansion of the Yff central triangle until the three outer triangles reduce to points on the sides of the triangle.
Any triangle △ ABC is the triangle formed by the lines which are externally tangent to the three excircles of the Yff central triangle of △ ABC .
Generalization of Yff centre of congruence