X3981

X305com(1st BROCARD TRIANGLE)

X3981 = X305-of-1st-Brocard-triangle
< 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) { 6, 25 }: Central Line L(6, 25) { 2, 694 }: Central Line L(2, 694) { 4, 695 }: Central Line L(4, 695) { 305, 698 }: Central Line L(305, 698) { 23, 1501 }: Central Line L(23, 1501) { 511, 1196 }: Central Line L(511, 1196) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_2 = CENTROID (0.5374, 0.2000) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_4 = ORTHOCENTER (0.6122, 0.3958) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_698 = EVEN (- 4, - 2) INFINITY POINT (1.0503, 0.4852) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_1501 = TRILINEAR 5th POWER POINT (0.6596, 0.3922) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1196 = 3rd SARAGOSSA POINT OF X(25) (0.6432, 0.2801) X_3981 = com(1st BROCARD TRIANGLE) (0.5850, 0.1839) A B C X6 X25 X2 X694 X4 X695 X305 X698 X23 X1501 X511 X1196 X3981 (a, b, c) = (5, 6, 7) | AB = 1

X3981 (X305com(1st BROCARD 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 \(f(a,b,c) = a^{2}(b^{4} + c^{4} - b^{2}c^{2})\)
Search Value (6, 9, 13): \(1.723095105238\)
▸ Incident Central Lines15 lines

{2, 694}, {4, 695}, {6, 25}, {22, 1691}, {23, 1501}, {305, 698}, {386, 2653}, {493, 1584}, {494, 1583}, {511, 1196}, {1350, 1611}, {1993, 2056}, {2979, 3231}, {3051, 3060}, {3095, 3117}

▸ Functional Relations2 relations