X3880

X519com[INVERSE(n(3rd EULER TRIANGLE))]

X3880 = isogonal conjugate of X8686
< 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) { 65, 145 }: Central Line L(65, 145) { 8, 210 }: Central Line L(8, 210) { 1, 474 }: Central Line L(1, 474) { 10, 496 }: Central Line L(10, 496) { 30, 511 }: Central Line L(30, 511) { 100, 1319 }: Central Line L(100, 1319) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1 = INCENTER (0.5714, 0.2333) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_3880 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.0459, 0.4930) A B C X65 X145 X8 X210 X1 X474 X10 X496 X30 X511 X100 X1319 X3880 (a, b, c) = (5, 6, 7) | AB = 1

X3880 (X519com[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 \(f(a,b,c) = a(b + c - a)(b^{2} + c^{2} + ab + ac - 4bc)\)
▸ Linear Combinations1 combination
▸ Incident Central Lines25 lines

{1, 474}, {8, 210}, {10, 496}, {30, 511}, {36, 2932}, {37, 3169}, {65, 145}, {72, 3586}, {78, 2098}, {100, 1319}, {354, 3241}, {392, 3679}, {644, 2348}, {942, 3244}, {958, 1697}, {1145, 1737}, {1212, 3208}, {1318, 1320}, {1616, 1722}, {1875, 1897}, {1898, 3621}, {2170, 3693}, {3555, 3633}, {3616, 3698}, {3635, 3754}

▸ Functional Relations2 relations