X3211

X57-CEVA CONJUGATE OF X3

X3211 = crosssum of X650 and X2969
< 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) { 3, 48 }: Central Line L(3, 48) { 6, 169 }: Central Line L(6, 169) { 155, 610 }: Central Line L(155, 610) { 651, 1119 }: Central Line L(651, 1119) { 579, 2178 }: Central Line L(579, 2178) { 1467, 1743 }: Central Line L(1467, 1743) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1119 = 2nd HATZIPOLAKIS PERSPECTOR (0.6322, 0.5039) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_2178 = -ISOCONJUGATE OF X(90) (0.6843, 0.4716) X_1467 = -BETH CONJUGATE OF X(938) (0.6380, 0.3556) X_1743 = MIMOSA TRANSFORM OF X(222) (0.6798, 0.3620) X_3211 = -CEVA CONJUGATE OF X(3) (1.0919, 0.4254) A B C X57 X3 X48 X6 X169 X155 X610 X651 X1119 X579 X2178 X1467 X1743 X3211 (a, b, c) = (5, 6, 7) | AB = 1

X3211 (X57-CEVA CONJUGATE OF X3) 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 \(x : y : z\) = X57 and \(u : v : w\) = X3
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(2.230267073061\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a(b^{2} + c^{2} - a^{2})[a^{4} - 2a^{3}(b + c) - 2a^{2}bc + 2a(b^{3} + c^{3}) - (b^{2} - c^{2})^{2}] (E\). Danneels)

▸ Incident Central Lines9 lines

{3, 48}, {6, 169}, {57, 3173}, {155, 610}, {579, 2178}, {651, 1119}, {1069, 2164}, {1200, 2280}, {1467, 1743}

▸ Functional Relations2 relations