Yff triangles

Let three isoscelizers I_(A C) I_(A B), I_(B A) I_(B C), and I_(C A) I_(C B) be constructed on a triangle Δ A B C, one for each side. This makes all of the inner triangles similar to each other. However, there is a unique set of three isoscelizers for which the four interior triangles Δ A' I_(B C) I_(C B), Δ I_(A C) B' I_(C A), Δ I_(A B) I_(B A) C', and Δ A' B' C' are congruent. The innermost triangle Δ A' B' C' is called the Yff central triangle.

extangents triangle | isoscelizer | Yff center of congruence | Yff central circle