X3923

X1com(1st BROCARD TRIANGLE)

X3923 = anticomplement of X3821
< 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) { 4, 9 }: Orthocenter–Spieker Line { 1, 87 }: Central Line L(1, 87) { 75, 238 }: Central Line L(75, 238) { 31, 321 }: Central Line L(31, 321) { 58, 314 }: Central Line L(58, 314) { 171, 312 }: Central Line L(171, 312) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_3923 = com[1st BROCARD TRIANGLE))] (0.5293, 0.2039) A B C X4 X9 X1 X87 X75 X238 X31 X321 X58 X314 X171 X312 X3923 (a, b, c) = (5, 6, 7) | AB = 1

X3923 (X1com(1st BROCARD 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 \(f(a,b,c) = a^{3} + b^{2}c + bc^{2}\)
Search Value (6, 9, 13): \(2.748228870271\)
▸ Incident Central Lines36 lines

{1, 87}, {2, 846}, {4, 9}, {6, 740}, {8, 1757}, {20, 2944}, {31, 321}, {44, 3696}, {55, 1215}, {58, 314}, {63, 3741}, {75, 238}, {76, 1966}, {171, 312}, {182, 2783}, {190, 984}, {226, 3771}, {256, 1008}, {386, 1045}, {519, 1992}, {536, 1386}, {537, 3242}, {752, 3416}, {896, 1150}, {936, 1721}, {964, 2292}, {988, 1125}, {990, 997}, {996, 2802}, {1009, 1284}, {1352, 2792}, {1468, 3702}, {1836, 2887}, {2308, 3187}, {2795, 3734}, {3175, 3745}

▸ Functional Relations4 relations