X2341

X2-ISOCONJUGATE OF X1464

X2341 = polar conjugate of isotomic conjugate of X1793
< 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) { 6, 13 }: Central Line L(6, 13) { 37, 101 }: Central Line L(37, 101) { 81, 226 }: Central Line L(81, 226) { 312, 645 }: Central Line L(312, 645) { 80, 1172 }: Central Line L(80, 1172) { 9, 1793 }: Central Line L(9, 1793) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_645 = BARYCENTRIC MULTIPLIER FOR KIEPERT PARABOLA (-0.0375, 0.2992) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1793 = INVERSE MIMOSA TRANSFORM OF X(30) (0.7938, -0.0219) X_2341 = -ISOCONJUGATE OF X(1464) (0.8872, -0.0824) A B C X6 X13 X37 X101 X81 X226 X312 X645 X80 X1172 X9 X1793 X2341 (a, b, c) = (5, 6, 7) | AB = 1

X2341 (X2-ISOCONJUGATE OF X1464) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X1464
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(2.696282603872\)
▸ Incident Central Lines11 lines

{6, 13}, {9, 1793}, {37, 101}, {80, 1172}, {81, 226}, {163, 2265}, {210, 2328}, {312, 645}, {644, 2287}, {1725, 2159}, {2222, 2249}

▸ Functional Relations5 relations