X3891

X2887com[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, 321 }: Central Line L(1, 321) { 145, 388 }: Central Line L(145, 388) { 31, 726 }: Central Line L(31, 726) { 38, 1150 }: Central Line L(38, 1150) { 2, 1390 }: Central Line L(2, 1390) { 100, 1403 }: Central Line L(100, 1403) 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_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1150 = INTERSECTION OF LINES X(2)X(6) AND X(3)X(8) (0.4725, 0.1302) X_2 = CENTROID (0.5374, 0.2000) X_1390 = ISOGONAL CONJUGATE OF X(1386) (0.5559, 0.2165) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1403 = -BETH CONJUGATE OF X(43) (0.6606, 0.3972) X_3891 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.7447, 0.3859) A B C X1 X321 X145 X388 X31 X726 X38 X1150 X2 X1390 X100 X1403 X3891 (a, b, c) = (5, 6, 7) | AB = 1

X3891 (X2887com[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 \(f(a,b,c) = a^{3} + ab^{2} + ac^{2} - b^{2}c - bc^{2}\)
Search Value (6, 9, 13): \(-2.154040506641\)
▸ Incident Central Lines15 lines

{1, 321}, {2, 1390}, {31, 726}, {38, 1150}, {76, 3112}, {100, 1403}, {145, 388}, {192, 1621}, {239, 3681}, {278, 1280}, {518, 3187}, {536, 3744}, {1255, 3616}, {1279, 3175}, {1824, 3555}