X3420

X1-VERTEX CONJUGATE OF X9

X3420 = isogonal conjugate of X3421
< 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) { 25, 104 }: Central Line L(25, 104) { 3, 392 }: Central Line L(3, 392) { 859, 1444 }: Central Line L(859, 1444) { 1450, 2122 }: Central Line L(1450, 2122) { 2163, 2291 }: Central Line L(2163, 2291) { 1811, 2932 }: Central Line L(1811, 2932) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3421 = ISOGONAL CONJUGATE OF X(3420) (0.4271, 0.0555) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_859 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(81) (1.1279, 1.7448) X_1444 = -BETH CONJUGATE OF X(332) (0.4762, 0.0921) X_1450 = -BETH CONJUGATE OF X(392) (0.6088, 0.2886) X_2122 = EIGENTRANSFORM OF X(8) (0.3815, -2.1505) X_2163 = -ISOCONJUGATE OF X(45) (0.6195, 0.3035) X_2291 = -ISOCONJUGATE OF X(1155) (0.9245, -0.1812) X_1811 = INVERSE MIMOSA TRANSFORM OF X(519) (1.5714, 0.1077) X_2932 = TANGENTIAL-ISOGONAL CONJUGATE OF X(36) (-0.1579, 0.7735) X_3420 = -VERTEX CONJUGATE OF X(9) (0.6259, 0.4717) A B C X3421 X25 X104 X3 X392 X859 X1444 X1450 X2122 X2163 X2291 X1811 X2932 X3420 (a, b, c) = (5, 6, 7) | AB = 1

X3420 (X1-VERTEX CONJUGATE OF X9) 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 \(f(a,b,c) = a/[a^{2}vwyz - ux(bw + cv)(bz + cy)]\), where \(u : v : w\) = X1 and \(x : y : z\) = X9
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.040580038922\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines6 lines

{3, 392}, {25, 104}, {859, 1444}, {1450, 2122}, {1811, 2932}, {2163, 2291}

▸ Functional Relations1 relation