X3196

X36-CEVA CONJUGATE OF X55

X3196 = crosssum of X650 and X3025
< 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) { 36, 44 }: Central Line L(36, 44) { 45, 55 }: Central Line L(45, 55) { 6, 101 }: Central Line L(6, 101) { 9, 1030 }: Central Line L(9, 1030) { 198, 2265 }: Central Line L(198, 2265) { 909, 3207 }: Central Line L(909, 3207) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1030 = ISOGONAL CONJUGATE OF X(1029) (0.5271, 0.1468) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_2265 = -ISOCONJUGATE OF X(953) (-3.6429, 5.2489) X_909 = POINT ADHAFERA (0.9286, -0.3499) X_3207 = -CEVA CONJUGATE OF X(6) (0.5198, 0.0728) X_3196 = -CEVA CONJUGATE OF X(55) (-0.1579, 0.7735) A B C X36 X55 X44 X45 X6 X101 X9 X1030 X198 X2265 X909 X3207 X3196 (a, b, c) = (5, 6, 7) | AB = 1

X3196 (X36-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 \(x : y : z\) = X36 and \(u : v : w\) = X55
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(1.569669688212\)
▸ Incident Central Lines6 lines

{6, 101}, {9, 1030}, {36, 44}, {45, 55}, {198, 2265}, {909, 3207}

▸ Functional Relations4 relations