X3429

X3-VERTEX CONJUGATE OF X10

X3429 = isogonal conjugate of X3430
< 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, 1503 }: Central Line L(10, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3430 = ISOGONAL CONJUGATE OF X(3429) (0.3893, -0.0808) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1503 = POINT ARKAB (0.4818, -0.3843) X_3429 = -VERTEX CONJUGATE OF X(10) (0.5862, 0.8739) A B C X3430 X10 X1503 X3429 (a, b, c) = (5, 6, 7) | AB = 1

X3429 (X3-VERTEX CONJUGATE OF X10) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/[a^{2}vwyz - ux(bw + cv)(bz + cy)] :\), where \(u : v : w\) = X3 and \(x : y : z\) = X10
Barycentrics: \(1/[a^{5} + a^{3}bc + a^{2}(b + c)(2b^{2} - bc + 2c^{2}) - a(b + c)^{2}(b^{2} - bc + c^{2}) - (b + c)(2b^{4} - b^{3}c + 2b^{2}c^{2} - bc^{3} + 2c^{4})] : : (E. Danneels)\)
Search Value (6, 9, 13): \(-99.226870347912\)

X3429 lies on the Kiepert hyperbola.

▸ Incident Central Lines1 line

{10, 1503}

▸ Functional Relations1 relation