X3878

X140com[INVERSE(n(4th EULER TRIANGLE))]

X3878 = X80-of-X1-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) { 5, 10 }: Central Line L(5, 10) { 1, 21 }: Central Line L(1, 21) { 8, 80 }: Central Line L(8, 80) { 3, 214 }: Central Line L(3, 214) { 65, 392 }: Central Line L(65, 392) { 72, 519 }: Central Line L(72, 519) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_8 = NAGEL POINT (0.4694, 0.1333) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_3878 = com[INVERSE(n(4th EULER TRIANGLE))] (0.4878, 0.1233) A B C X5 X10 X1 X21 X8 X80 X3 X214 X65 X392 X72 X519 X3878 (a, b, c) = (5, 6, 7) | AB = 1

X3878 (X140com[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 \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c + 2abc)\)
Search Value (6, 9, 13): \(4.259481129957\)
▸ Linear Combinations1 combination
▸ Incident Central Lines32 lines

{1, 21}, {2, 3754}, {3, 214}, {5, 10}, {8, 80}, {9, 1389}, {40, 997}, {65, 392}, {72, 519}, {101, 3496}, {210, 3626}, {213, 3727}, {354, 3636}, {404, 484}, {405, 2099}, {518, 3244}, {551, 942}, {759, 1098}, {944, 2801}, {956, 2098}, {958, 1482}, {986, 995}, {1201, 3670}, {1320, 3467}, {1829, 1904}, {2176, 3735}, {2922, 3556}, {3061, 3730}, {3230, 3721}, {3555, 3635}, {3632, 3681}, {3634, 3753}

▸ Functional Relations5 relations