X3625

H⁻¹(X1; M, -1/2)

X3625 = {X1,X8}-harmonic conjugate of X3626
< 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, 8 }: Nagel Line { 1, 2 }: Nagel Line { 548, 952 }: Central Line L(548, 952) { 536, 1358 }: Central Line L(536, 1358) { 515, 1657 }: Central Line L(515, 1657) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3626 = H-1(X(1); M, -2) (0.4949, 0.1583) X_1 = INCENTER (0.5714, 0.2333) X_8 = NAGEL POINT (0.4694, 0.1333) X_2 = CENTROID (0.5374, 0.2000) X_548 = MIDPOINT OF X(5) AND X(20) (0.4719, 0.0286) X_952 = INTERSECTION OF X(1)X(5) AND X(3)X(8) (0.1267, 0.6191) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_1358 = BRISSE TRANSFORM OF X(101) (0.7869, 0.1440) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1657 = {X(3),X(4)}-HARMONIC CONJUGATE OF X(1656) (0.2755, -0.4853) X_3625 = H-1(X(1); M, -1/2) (0.4184, 0.0833) A B C X3626 X1 X8 X2 X548 X952 X536 X1358 X515 X1657 X3625 (a, b, c) = (5, 6, 7) | AB = 1

X3625 (H⁻¹(X1; M, -1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(4a - 3b - 3c) : :\)
Barycentrics: \(4a - 3b - 3c : 4b - 3c - 3a : 4c - 3a - 3b\)
Search Value (6, 9, 13): \(5.916079783100\)
▸ Alternate Coordinates1 form

  • Trilinears: \(7 r - 6 R \sin B \sin C : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines6 lines

{1, 2}, {44, 2321}, {72, 2802}, {515, 1657}, {536, 1358}, {548, 952}

▸ Functional Relations2 relations