X3432

X5-VERTEX CONJUGATE OF X5

X3432 = isogonal conjugate of X2888
< 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) { 49, 52 }: Central Line L(49, 52) { 5, 1601 }: Central Line L(5, 1601) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2888 = ANTICOMPLEMENTARY CONJUGATE OF X(3) (0.4361, 0.1647) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1601 = TCC-PERSPECTOR OF X(5) (0.4370, 0.2016) X_3432 = -VERTEX CONJUGATE OF X(5) (0.6629, 0.2913) A B C X2888 X49 X52 X5 X1601 X3432 (a, b, c) = (5, 6, 7) | AB = 1

X3432 (X5-VERTEX CONJUGATE OF X5) 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 \(u : v : w\) = X5 and \(x : y : z\) = X5
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.117761763908\)
▸ Alternate Coordinates2 forms

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where g(a,b,c)

  • Barycentrics: \(a^{2}/[a^{10} - 3a^{8}(b^{2} + c^{2}) + a^{6}(4b^{4} + 5b^{2}c^{2} + 4c^{4}) - 2a^{4}(b^{2} + c^{2})(2b^{4} - b^{2}c^{2} + 2c^{4}) + 3a^{2}(b^{2} - c^{2})^{2}(b^{4} + b^{2}c^{2} + c^{4}) - (b^{2} + c^{2})(b^{2} - c^{2})^{4}] (E. Danneels)\)

▸ Incident Central Lines2 lines

{5, 1601}, {49, 52}

▸ Functional Relations2 relations