X3901

X550com[INVERSE(n(3rd 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) { 1, 21 }: Central Line L(1, 21) { 72, 1698 }: Central Line L(72, 1698) { 517, 1657 }: Central Line L(517, 1657) { 519, 1770 }: Central Line L(519, 1770) { 78, 3336 }: Central Line L(78, 3336) { 79, 3419 }: Central Line L(79, 3419) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1657 = {X(3),X(4)}-HARMONIC CONJUGATE OF X(1656) (0.2755, -0.4853) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_1770 = MIMOSA TRANSFORM OF X(943) (0.6554, 0.4275) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_3419 = ISOGONAL CONJUGATE OF X(3418) (0.4918, 0.1745) X_3901 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.9061, 0.6732) A B C X1 X21 X72 X1698 X517 X1657 X519 X1770 X78 X3336 X79 X3419 X3901 (a, b, c) = (5, 6, 7) | AB = 1

X3901 (X550com[INVERSE(n(3rd 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 \(f(a,b,c) = a(2b^{3} + 2c^{3} -2a^{2}b - 2a^{2}c - abc)\)
Search Value (6, 9, 13): \(-8.586381972541\)
▸ Linear Combinations1 combination
▸ Incident Central Lines11 lines

{1, 21}, {65, 3679}, {72, 1698}, {78, 3336}, {79, 3419}, {517, 1657}, {518, 3632}, {519, 1770}, {942, 3624}, {997, 3337}, {3681, 3754}