X1035

ISOGONAL CONJUGATE OF X1034

X1035 is the isogonal conjugate of X1034.
< 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) { 25, 34 }: Central Line L(25, 34) { 55, 64 }: Central Line L(55, 64) { 3, 223 }: Central Line L(3, 223) { 6, 603 }: Central Line L(6, 603) { 222, 581 }: Central Line L(222, 581) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1034 = -CROSS CONJUGATE OF X(8) (0.3920, -0.4271) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) X_1035 = ISOGONAL CONJUGATE OF X(1034) (0.4590, -14.0277) A B C X1034 X25 X34 X55 X64 X3 X223 X6 X603 X222 X581 X1035 (a, b, c) = (5, 6, 7) | AB = 1

X1035 (ISOGONAL CONJUGATE OF X1034) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(w^{2}u^{2} + u^{2}v^{2} - v^{2}w^{2}) + 2uvw(au + bv + cw) \cos A\), where \(u : v : w\) = X329
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-0.201205090866\)
▸ Incident Central Lines5 lines

{3, 223}, {6, 603}, {25, 34}, {55, 64}, {222, 581}

▸ Functional Relations2 relations