X3842

X3688com(4th EULER TRIANGLE)

X3842 = complement of X24325
< 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, 38 }: Central Line L(2, 38) { 10, 37 }: Central Line L(10, 37) { 1, 872 }: Central Line L(1, 872) { 75, 1089 }: Central Line L(75, 1089) { 518, 1125 }: Central Line L(518, 1125) { 86, 1757 }: Central Line L(86, 1757) 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_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_1757 = MIMOSA TRANSFORM OF X(295) (2.6667, 2.7217) X_3842 = com(4th EULER TRIANGLE) (0.5386, 0.1996) A B C X2 X38 X10 X37 X1 X872 X75 X1089 X518 X1125 X86 X1757 X3842 (a, b, c) = (5, 6, 7) | AB = 1

X3842 (X3688com(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 \(f(a,b,c) = (b + c)(a^{2} + 2ab + 2ac + bc)\)
Search Value (6, 9, 13): \(2.594861155582\)
▸ Incident Central Lines11 lines

{1, 872}, {2, 38}, {10, 37}, {75, 1089}, {86, 1757}, {333, 1961}, {518, 1125}, {726, 3634}, {1237, 1921}, {2664, 3736}, {2667, 3293}

▸ Functional Relations1 relation

  • X3842 = complement of X24325