X3179

X13-CEVA CONJUGATE OF X1

X3179 = X13-Ceva conjugate of X1
< 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, 15 }: Central Line L(1, 15) { 9, 46 }: Central Line L(9, 46) { 13, 484 }: Central Line L(13, 484) { 57, 1081 }: Central Line L(57, 1081) { 18, 1653 }: Central Line L(18, 1653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_1 = INCENTER (0.5714, 0.2333) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1081 = POINT ALPHECCA (0.6056, 0.3226) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_1653 = 5th EVANS PERSPECTOR (0.6584, 0.3759) X_3179 = -CEVA CONJUGATE OF X(1) (0.6082, 0.3189) A B C X13 X1 X15 X9 X46 X484 X57 X1081 X18 X1653 X3179 (a, b, c) = (5, 6, 7) | AB = 1

X3179 (X13-CEVA CONJUGATE OF X1) 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 \(x : y : z\) = X13 and \(u : v : w\) = X1
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): \(0.034314953584\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\tan(A/2 + \pi /6) : \tan(B/2 + \pi /6) : \tan(C/2 + \pi /6)\) (M. Iliev, 4/12/07)

▸ Incident Central Lines5 lines

{1, 15}, {9, 46}, {13, 484}, {18, 1653}, {57, 1081}

▸ Functional Relations2 relations