X3893

X3626com[INVERSE(n(4th EULER 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) { 8, 210 }: Central Line L(8, 210) { 145, 354 }: Central Line L(145, 354) { 65, 519 }: Central Line L(65, 519) { 382, 517 }: Central Line L(382, 517) { 518, 1278 }: Central Line L(518, 1278) { 55, 2136 }: Central Line L(55, 2136) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_354 = WEILL POINT (0.5823, 0.2533) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1278 = CONGRUENT MIDWAY-PARALLELIANS POINT (0.3828, 0.0729) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2136 = EIGENTRANSFORM OF X(57) (0.8750, 0.4082) X_3893 = com[INVERSE(n(4th EULER TRIANGLE))] (0.4000, 0.0933) A B C X8 X210 X145 X354 X65 X519 X382 X517 X518 X1278 X55 X2136 X3893 (a, b, c) = (5, 6, 7) | AB = 1

X3893 (X3626com[INVERSE(n(4th 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 \(f(a,b,c) = a(b + c - a)(b^{2} + c^{2} + ab + ac - 6bc)\)
Search Value (6, 9, 13): \(6.164088011695\)
▸ Incident Central Lines14 lines

{1, 3689}, {8, 210}, {55, 2136}, {65, 519}, {72, 2802}, {145, 354}, {200, 2098}, {382, 517}, {392, 3626}, {518, 1278}, {942, 3633}, {1697, 3683}, {1706, 3304}, {3244, 3753}