X3608

1st MORLEY-GIBERT PERSPECTOR

X3608 is the perspector of the Morley triangle and the triangle of the cusps of the Steiner deltoid. (Bernard Gibert, November 3, 2010). See
< 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, 356 }: Central Line L(5, 356) { 20, 3278 }: Central Line L(20, 3278) { 631, 3279 }: Central Line L(631, 3279) { 3273, 3609 }: Central Line L(3273, 3609) 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_356 = MORLEY CENTER (0.5727, 0.2361) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3278 = PERSPECTOR OF TRIANGLES M1M2M3 AND T1T2T3 (0.5622, 0.2166) X_631 = 3/5*OG (0.5224, 0.1608) X_3279 = PERSPECTOR OF TRIANGLES M1M2M3 AND N1N2N3 (0.5876, 0.2634) X_3273 = PERSPECTOR OF TRIANGLES M1M2M3 AND J1J2J3 (0.5744, 0.2367) X_3609 = 2nd MORLEY-GIBERT PERSPECTOR (0.5666, 0.2382) X_3608 = 1st MORLEY-GIBERT PERSPECTOR (0.5710, 0.2374) A B C X5 X356 X20 X3278 X631 X3279 X3273 X3609 X3608 (a, b, c) = (5, 6, 7) | AB = 1

X3608 (1st 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 \(f(A,B,C) = \cos A + 2 \cos B \cos C + 3 \cos(A/3) + 6 \cos(B/3) \cos(C/3)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.566059588797\)
▸ Incident Central Lines4 lines

{5, 356}, {20, 3278}, {631, 3279}, {3273, 3609}