X3783

X668com[T(bc, c²)]

< 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 { 87, 193 }: Central Line L(87, 193) { 72, 695 }: Central Line L(72, 695) { 291, 518 }: Central Line L(291, 518) { 350, 740 }: Central Line L(350, 740) { 668, 730 }: Central Line L(668, 730) 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_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_730 = EVEN (- 2, 1) INFINITY POINT (0.0843, -0.1730) X_3783 = com[T(bc, c2)] (4.1101, 3.7005) A B C X1 X2 X87 X193 X72 X695 X291 X518 X350 X740 X668 X730 X3783 (a, b, c) = (5, 6, 7) | AB = 1

X3783 (X668com[T(bc, c²)]) 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 \(f(a,b,c) = a(a^{2} - bc)(b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(-16.567029693580\)
▸ Incident Central Lines16 lines

{1, 2}, {69, 1740}, {72, 695}, {87, 193}, {100, 2239}, {238, 1914}, {291, 518}, {319, 1964}, {320, 2234}, {350, 740}, {668, 730}, {672, 1282}, {752, 2230}, {788, 1491}, {984, 2276}, {1654, 2309}