X3204

X54-CEVA CONJUGATE OF X55

X3204 = X54-Ceva conjugate of X55
< 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, 101 }: Central Line L(6, 101) { 45, 284 }: Central Line L(45, 284) { 41, 584 }: Central Line L(41, 584) { 218, 583 }: Central Line L(218, 583) { 9, 2174 }: Central Line L(9, 2174) { 220, 2301 }: Central Line L(220, 2301) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_584 = ORTHOHARMONIC OF X(500) (0.5720, 0.2209) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2174 = -ISOCONJUGATE OF X(79) (0.5728, 0.2013) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_2301 = -ISOCONJUGATE OF X(1242) (0.5576, 0.1836) X_3204 = -CEVA CONJUGATE OF X(55) (0.6369, 0.2426) A B C X54 X55 X6 X101 X45 X284 X41 X584 X218 X583 X9 X2174 X220 X2301 X3204 (a, b, c) = (5, 6, 7) | AB = 1

X3204 (X54-CEVA CONJUGATE OF X55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X54 and \(u : v : w\) = X55
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.435563055986\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a[a^{3} - a(b + c)^{2} + bc(b + c)] (E\). Danneels)

▸ Incident Central Lines8 lines

{6, 101}, {9, 2174}, {41, 584}, {45, 284}, {218, 583}, {220, 2301}, {1953, 2246}, {2176, 2220}

▸ Functional Relations1 relation