X203

X1-CEVA CONJUGATE OF X16

X203 = X1-Ceva conjugate of X16
< 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) { 11, 14 }: Central Line L(11, 14) { 12, 17 }: Feuerbach Line { 16, 36 }: Central Line L(16, 36) { 1, 61 }: Feuerbach Line { 15, 55 }: Central Line L(15, 55) { 6, 101 }: Central Line L(6, 101) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) 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_203 = -CEVA CONJUGATE OF X(16) (0.4136, 0.3918) A B C X1 X16 X11 X14 X12 X17 X36 X61 X15 X55 X6 X101 X203 (a, b, c) = (5, 6, 7) | AB = 1

X203 (X1-CEVA CONJUGATE OF X16) 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 \(f(A,B,C) = u(v + w - u)\), \(u = u(A,B,C) = \sin(A - \pi /3)\), \(v = u(B,C,A)\), \(w = u(C,A,B)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.122831801616\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1 + \cos(A + 2\pi /3) : 1 + \cos(B + 2\pi /3) : 1 + \cos(C + 2\pi /3)\) (Joe Goggins, Oct. 19, 2005)

▸ Incident Central Lines10 lines

{1, 61}, {6, 101}, {11, 14}, {12, 17}, {15, 55}, {16, 36}, {18, 499}, {56, 62}, {396, 495}, {398, 496}

▸ Functional Relations1 relation