X678

CROSSPOINT OF X1 AND X44

X678 is the crosspoint of X1 and X44.
< 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) { 1, 88 }: Central Line L(1, 88) { 45, 55 }: Central Line L(45, 55) { 44, 902 }: Central Line L(44, 902) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) A B C X1 X44 X88 X45 X55 X902 X678 (a, b, c) = (5, 6, 7) | AB = 1

X678 (CROSSPOINT OF X1 AND X44) 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 \(f(a,b,c) = (b + c - 2a)^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(2.169048499762\)

X678 lies on the incentral inellipse (a.k.a. Hofstadter ellipse E(1/2)).

▸ Incident Central Lines3 lines

{1, 88}, {44, 902}, {45, 55}

▸ Functional Relations6 relations