X400

YFF-MALFATTI POINT

In 1997, Yff considered the configuration for the 1st Ajima-Malfatti point, X179. He proved that the same tangencies are possible in another way if the circles are not required to lie inside ABC. With tangency points labeled as before, the lines AA', BB', CC' concur in X400.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_400 = YFF-MALFATTI POINT (0.3372, 0.0569) A B C X400 (a, b, c) = (5, 6, 7) | AB = 1

X400 (YFF-MALFATTI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Trilinears: \(\csc^{4}(A/4) : \csc^{4}(B/4) : \csc^{4}(C/4)\)
Barycentrics: \(\sin A \csc^{4}(A/4) : \sin B \csc^{4}(B/4) : \sin C \csc^{4}(C/4)\)
Search Value (6, 9, 13): \(6.277848902687\)