X180

2nd AJIMA-MALFATTI POINT

Let A″,B″,C″ be the excenters of ABC, and let A',B',C' be as in the construction of X179. The lines A'A″,B'B″,B'B″ concur in X180. Trilinears are found in Yff’s unpublished notes. See X179.
< 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) { 173, 483 }: Central Line L(173, 483) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_483 = RADICAL CENTER OF AJIMA-MALFATTI CIRCLES (0.5762, 0.2431) X_180 = 2nd AJIMA-MALFATTI POINT (0.5840, 0.2581) A B C X173 X483 X180 (a, b, c) = (5, 6, 7) | AB = 1

X180 (2nd AJIMA-MALFATTI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1/t(B,C,A) + 1/t(C,B,A) - 1/t(A,C,B)\), \(t(A,B,C) = 1 + 2(\sec A/4 \cos B/4 \cos C/4)^{2}\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A)f(A,B,C)\)
Search Value (6, 9, 13): \(1.184017677850\)
▸ Incident Central Lines1 line

{173, 483}