X3850

X140com(EULER TRIANGLE)

X3850 = midpoint of X4 and X140
< 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) { 4, 140 }: Euler Line { 2, 3 }: Euler Line { 399, 1199 }: Central Line L(399, 1199) { 355, 3633 }: Central Line L(355, 3633) { 946, 3625 }: Central Line L(946, 3625) { 952, 3635 }: Central Line L(952, 3635) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_399 = PARRY REFLECTION POINT (0.0032, 0.9936) X_1199 = 3rd SARAGOSSA POINT OF X(54) (0.5984, 0.2504) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_3633 = H-1(X(8); M, -1/2) (0.7755, 0.4332) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_3625 = H-1(X(1); M, -1/2) (0.4184, 0.0833) X_952 = INTERSECTION OF X(1)X(5) AND X(3)X(8) (0.1267, 0.6191) X_3635 = H-1(X(10); M, -1/2) (0.5969, 0.2583) X_3850 = com(EULER TRIANGLE) (0.5702, 0.2856) A B C X4 X140 X2 X3 X399 X1199 X355 X3633 X946 X3625 X952 X3635 X3850 (a, b, c) = (5, 6, 7) | AB = 1

X3850 (X140com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(2a^{4} - 5b^{4} - 5c^{4} + 3a^{2}b^{2} + 3a^{2}c^{2} + 10b^{2}c^{2} : :\)
Search Value (6, 9, 13): \(-1.004501046505\)
▸ Linear Combinations1 combination
▸ Incident Central Lines8 lines

{2, 3}, {355, 3633}, {399, 1199}, {946, 3625}, {952, 3635}, {1327, 3594}, {1328, 3592}, {3583, 3614}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X3850 has Shinagawa coefficients \((3, 7)\).