X3012

(ORTHIC AXIS)∩(SODDY LINE)

< 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) { 1, 7 }: Soddy Line { 230, 231 }: Central Line L(230, 231) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_3012 = (ORTHIC AXIS)∩(SODDY LINE) (0.7905, 0.7402) A B C X1 X7 X230 X231 X3012 (a, b, c) = (5, 6, 7) | AB = 1

X3012 ((ORTHIC AXIS)∩(SODDY LINE)) 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 \(f(A,B,C) = [\sec^{2}(A/2) - \sec^{2}(B/2)] \cos B + [\sec^{2}(A/2) - \sec^{2}(C/2)] \cos C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.749351217538\)
▸ Incident Central Lines2 lines

{1, 7}, {230, 231}