X3831

X3702com(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) { 1, 2 }: Nagel Line { 312, 986 }: Central Line L(312, 986) { 141, 1329 }: Central Line L(141, 1329) { 750, 964 }: Central Line L(750, 964) { 726, 1089 }: Central Line L(726, 1089) { 942, 1215 }: Central Line L(942, 1215) 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_2 = CENTROID (0.5374, 0.2000) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_964 = INTERCEPT OF EULER LINE AND LINE X(6)X(8) (0.5394, 0.2050) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_942 = INCIRCLE-INVERSE OF X(36) (0.5878, 0.2633) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_3831 = com(4th EULER TRIANGLE) (0.5082, 0.1713) A B C X1 X2 X312 X986 X141 X1329 X750 X964 X726 X1089 X942 X1215 X3831 (a, b, c) = (5, 6, 7) | AB = 1

X3831 (X3702com(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 \(f(a,b,c) = a^{2}b^{2} + a^{2}c^{2} + ab^{3} + ac^{3} + b^{3}c + bc^{3} + 2b^{2}c^{2}\)
Search Value (6, 9, 13): \(3.384522988895\)
▸ Incident Central Lines14 lines

{1, 2}, {5, 2887}, {38, 3701}, {141, 1329}, {312, 986}, {726, 1089}, {750, 964}, {942, 1215}, {992, 3686}, {1861, 3144}, {2277, 2321}, {2392, 3142}, {3663, 3760}, {3714, 3752}