X3757

X846com[INVERSE(n(1st BROCARD TRIANGLE))]

< 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) { 1, 2 }: Nagel Line { 25, 92 }: Central Line L(25, 92) { 55, 75 }: Central Line L(55, 75) { 183, 322 }: Central Line L(183, 322) { 333, 518 }: Central Line L(333, 518) { 31, 894 }: Central Line L(31, 894) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_322 = ISOTOMIC CONJUGATE OF X(84) (0.3430, -0.0168) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_3757 = com[INVERSE(n(1st BROCARD TRIANGLE))] (0.5109, 0.1740) A B C X1 X2 X25 X92 X55 X75 X183 X322 X333 X518 X31 X894 X3757 (a, b, c) = (5, 6, 7) | AB = 1

X3757 (X846com[INVERSE(n(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 \(f(a,b,c) = a^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} - abc\)
Search Value (6, 9, 13): \(3.494133597746\)
▸ Incident Central Lines19 lines

{1, 2}, {25, 92}, {31, 894}, {55, 75}, {69, 3475}, {183, 322}, {192, 968}, {238, 1215}, {274, 2223}, {312, 1001}, {314, 2346}, {321, 1621}, {333, 518}, {675, 831}, {726, 846}, {1104, 1220}, {1281, 1283}, {1402, 1441}, {1909, 1965}