X3437

X10-VERTEX CONJUGATE OF X10

X3437 = isogonal conjugate of X1330
< 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) { 10, 199 }: Central Line L(10, 199) { 35, 228 }: Central Line L(35, 228) { 184, 386 }: Central Line L(184, 386) { 2174, 2200 }: Central Line L(2174, 2200) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2206 = -ISOCONJUGATE OF X(321) (0.6455, 0.3498) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_2174 = -ISOCONJUGATE OF X(79) (0.5728, 0.2013) X_2200 = -ISOCONJUGATE OF X(286) (0.5626, 0.1362) X_3437 = -VERTEX CONJUGATE OF X(10) (0.6236, 0.5238) A B C X2206 X6 X10 X199 X35 X228 X184 X386 X2174 X2200 X3437 (a, b, c) = (5, 6, 7) | AB = 1

X3437 (X10-VERTEX CONJUGATE OF X10) 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 \(u : v : w\) = X10 and \(x : y : z\) = X10
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.047007080663\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines4 lines

{10, 199}, {35, 228}, {184, 386}, {2174, 2200}

▸ Functional Relations3 relations