X3633

H⁻¹(X8; M, -1/2)

< 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 { 40, 548 }: Central Line L(40, 548) { 210, 1357 }: Central Line L(210, 1357) { 191, 1697 }: Central Line L(191, 1697) { 517, 1657 }: Central Line L(517, 1657) { 46, 2136 }: Central Line L(46, 2136) 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_40 = BEVAN POINT (0.4286, -0.0292) X_548 = MIDPOINT OF X(5) AND X(20) (0.4719, 0.0286) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5449, 0.1845) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1657 = {X(3),X(4)}-HARMONIC CONJUGATE OF X(1656) (0.2755, -0.4853) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_2136 = EIGENTRANSFORM OF X(57) (0.8750, 0.4082) X_3633 = H-1(X(8); M, -1/2) (0.7755, 0.4332) A B C X1 X2 X40 X548 X210 X1357 X191 X1697 X517 X1657 X46 X2136 X3633 (a, b, c) = (5, 6, 7) | AB = 1

X3633 (H⁻¹(X8; M, -1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(5a - 2b - 2c) : :\)
Barycentrics: \(5a - 2b - 2c : 5b - 2c - 2a : 5c - 2a - 2b\)
Search Value (6, 9, 13): \(-3.944053188733\)
▸ Alternate Coordinates1 form

  • Trilinears: \(7 r - 4 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines12 lines

{1, 2}, {40, 548}, {46, 2136}, {191, 1697}, {210, 1357}, {517, 1657}, {1317, 1420}, {1482, 1699}, {1483, 3576}, {1743, 2325}, {2093, 3189}, {3339, 3476}