X3805

X2786com[INVERSE(nT(bc,c²))]

X3805 = crossdifference of every pair of points on line X6X256
< 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) { 30, 511 }: Central Line L(30, 511) { 38, 661 }: Central Line L(38, 661) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_3805 = com[INVERSE(nT(bc,c2))] (1.0651, -0.0568) A B C X30 X511 X38 X661 X3805 (a, b, c) = (5, 6, 7) | AB = 1

X3805 (X2786com[INVERSE(nT(bc,c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(b - c)(a^{2} + bc)(b^{2} + c^{2} + bc) : :\)
▸ Incident Central Lines2 lines

{30, 511}, {38, 661}

▸ Functional Relations3 relations

Notes

X3805 is the infinite point of perspectrices of every pair of {ABC, Gemini triangle 32, Gemini triangle 34}. (Randy Hutson, January 15, 2019)