X3998

X1779com[INVERSE(n(INCENTRAL TRIANGLE))]

X3998 = isogonal conjugate of X5317
< 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) { 2, 37 }: Central Line L(2, 37) { 3, 63 }: Central Line L(3, 63) { 306, 307 }: Central Line L(306, 307) { 326, 394 }: Central Line L(326, 394) { 81, 1257 }: Central Line L(81, 1257) { 100, 1297 }: Central Line L(100, 1297) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_1257 = ISOGONAL CONJUGATE OF X(1104) (0.4843, 0.1638) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_3998 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.3173, 0.0191) A B C X2 X37 X3 X63 X306 X307 X326 X394 X81 X1257 X100 X1297 X3998 (a, b, c) = (5, 6, 7) | AB = 1

X3998 (X1779com[INVERSE(n(INCENTRAL 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 \(f(a,b,c) = a(b + c)(b^{2} + c^{2} - a^{2})^{2}\)
Search Value (6, 9, 13): \(5.182133786844\)
▸ Incident Central Lines13 lines

{2, 37}, {3, 63}, {81, 1257}, {100, 1297}, {213, 2221}, {306, 307}, {326, 394}, {518, 2352}, {1073, 3692}, {1108, 3187}, {1210, 2901}, {1331, 1801}, {2287, 3219}

▸ Functional Relations1 relation

  • X3998 = isogonal conjugate of X5317