X3853

X3627com(EULER TRIANGLE)

X3853 = anticomplement of X33923
< 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) { 2, 3 }: Euler Line { 1327, 3592 }: Central Line L(1327, 3592) { 1328, 3594 }: Central Line L(1328, 3594) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1327 = ARCTAN(3) KIEPERT POINT (0.5967, 0.3083) X_3592 = ISOGONAL CONJUGATE OF 1st DIXIT POINT (0.5737, 0.2238) X_1328 = ARCTAN(-3) KIEPERT POINT (0.4997, 1.5024) X_3594 = ISOGONAL CONJUGATE OF 2nd DIXIT POINT (0.6553, 0.3586) X_3853 = com(EULER TRIANGLE) (0.6403, 0.4692) A B C X2 X3 X4 X1327 X3592 X1328 X3594 X3853 (a, b, c) = (5, 6, 7) | AB = 1

X3853 (X3627com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 6a^{4} - 5b^{4} - 5c^{4} - a^{2}b^{2} - a^{2}c^{2} + 10b^{2}c^{2}\)
Search Value (6, 9, 13): \(-8.791364987207\)
▸ Linear Combinations1 combination
▸ Incident Central Lines3 lines

{2, 3}, {1327, 3592}, {1328, 3594}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X3853 has Shinagawa coefficients \((1, -9)\).