X3207

X55-CEVA CONJUGATE OF X6

X3207 = X55-Ceva conjugate of X6
< 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, 41 }: Central Line L(6, 41) { 3, 101 }: Central Line L(3, 101) { 36, 218 }: Central Line L(36, 218) { 1, 910 }: Central Line L(1, 910) { 31, 1191 }: Central Line L(31, 1191) { 169, 1385 }: Central Line L(169, 1385) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_1 = INCENTER (0.5714, 0.2333) X_910 = CROSSPOINT OF X(57) AND X(105) (1.3163, 2.5495) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1191 = 2nd SARAGOSSA POINT OF X(56) (0.6211, 0.2922) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1385 = MIDPOINT OF INCENTER AND CIRCUMCENTER (0.5357, 0.1677) X_3207 = -CEVA CONJUGATE OF X(6) (0.5198, 0.0728) A B C X55 X6 X41 X3 X101 X36 X218 X1 X910 X31 X1191 X169 X1385 X3207 (a, b, c) = (5, 6, 7) | AB = 1

X3207 (X55-CEVA CONJUGATE OF X6) 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 \(x : y : z\) = X55 and \(u : v : w\) = X6
Search Value (6, 9, 13): \(-678.377148462084\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a[3a^{2} - 2ab - 2ac - (b - c)^{2}] : : (E. Danneels)\)

▸ Incident Central Lines23 lines

{1, 910}, {3, 101}, {6, 41}, {31, 1191}, {36, 218}, {45, 2182}, {169, 1385}, {595, 1384}, {909, 3196}, {944, 1146}, {1030, 3197}, {1100, 2270}, {1190, 1617}, {1319, 2082}, {1334, 2272}, {1376, 2329}, {1388, 2170}, {1604, 1630}, {1616, 1914}, {1696, 2268}, {2053, 2110}, {2176, 2223}, {2242, 2271}

▸ Functional Relations6 relations