X3609

2nd MORLEY-GIBERT PERSPECTOR

X3609 is the perspector of the triangle of the cusps of the Steiner deltoid and the equilateral triangle J defined just before X3272. (Bernard Gibert, November 3, 2010)
< 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) { 5, 3272 }: Feuerbach Line { 20, 3334 }: Central Line L(20, 3334) { 631, 3335 }: Central Line L(631, 3335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5698, 0.2349) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3334 = PERSPECTOR OF TRIANGLES T1T2T3 AND J1J2J3 (0.5478, 0.1930) X_631 = 3/5*OG (0.5224, 0.1608) X_3335 = PERSPECTOR OF TRIANGLES N1N2N3 AND J1J2J3 (0.6296, 0.3489) X_3609 = 2nd MORLEY-GIBERT PERSPECTOR (0.5666, 0.2382) A B C X5 X3272 X20 X3334 X631 X3335 X3609 (a, b, c) = (5, 6, 7) | AB = 1

X3609 (2nd MORLEY-GIBERT PERSPECTOR) 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 \(f(A,B,C) = \cos A + 2 \cos B \cos C + 3 \sin(A/3+\pi /6) + 6 \sin(B/3) \sin(C/3)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.471706662907\)
▸ Incident Central Lines3 lines

{5, 3272}, {20, 3334}, {631, 3335}