X1033

X3-CEVA CONJUGATE OF X25

X1033 = isogonal conjugate of X1032
< 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) { 6, 64 }: Central Line L(6, 64) { 19, 56 }: Central Line L(19, 56) { 55, 204 }: Central Line L(55, 204) { 25, 393 }: Central Line L(25, 393) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_19 = CLAWSON POINT (0.6246, 0.4244) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_1033 = -CEVA CONJUGATE OF X(25) (0.5778, 0.9664) A B C X3 X25 X6 X64 X19 X56 X55 X204 X393 X1033 (a, b, c) = (5, 6, 7) | AB = 1

X1033 (X3-CEVA CONJUGATE OF X25) 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 \(u : v : w\) = X20
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): \(0.455803031070\)
▸ Incident Central Lines4 lines

{6, 64}, {19, 56}, {25, 393}, {55, 204}

▸ Functional Relations2 relations