X3729

X3056com(EXCENTRAL TRIANGLE)

X3729 = crosssum of PU(48)
< 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) { 9, 75 }: Central Line L(9, 75) { 1, 87 }: Central Line L(1, 87) { 8, 144 }: Central Line L(8, 144) { 7, 346 }: Central Line L(7, 346) { 57, 312 }: Central Line L(57, 312) { 63, 321 }: Central Line L(63, 321) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_8 = NAGEL POINT (0.4694, 0.1333) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_7 = GERGONNE POINT (0.5903, 0.2769) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_3729 = com(EXCENTRAL TRIANGLE) (0.4872, 0.1745) A B C X9 X75 X1 X87 X8 X144 X7 X346 X57 X312 X63 X321 X3729 (a, b, c) = (5, 6, 7) | AB = 1

X3729 (X3056com(EXCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2} - ab - ac + 2bc : :\)
Search Value (6, 9, 13): \(3.806149231085\)
▸ Incident Central Lines36 lines

{1, 87}, {2, 2415}, {6, 536}, {7, 346}, {8, 144}, {9, 75}, {10, 2996}, {37, 980}, {46, 1089}, {57, 312}, {63, 321}, {69, 527}, {76, 1423}, {78, 990}, {85, 728}, {86, 3247}, {101, 1958}, {141, 545}, {142, 344}, {148, 1654}, {193, 519}, {200, 1721}, {226, 345}, {239, 1278}, {341, 1706}, {385, 3550}, {522, 1027}, {664, 1419}, {940, 3175}, {975, 3159}, {1229, 1445}, {1909, 3208}, {1944, 2324}, {1975, 2329}, {2191, 2414}, {2999, 3210}

▸ Functional Relations6 relations