X3605

ISOGONAL CONJUGATE OF X356

X3605 is the isogonal conjugate of X356.
< 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) { 1507, 1508 }: Central Line L(1507, 1508) { 358, 3279 }: Central Line L(358, 3279) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_356 = MORLEY CENTER (0.5727, 0.2361) X_1507 = 1st MORLEY-GIBERT POINT (0.5772, 0.2446) X_1508 = 2nd MORLEY-GIBERT POINT (0.5684, 0.2271) X_358 = 2nd MORLEY-TAYLOR-MARR CENTER (0.5670, 0.2245) X_3279 = PERSPECTOR OF TRIANGLES M1M2M3 AND N1N2N3 (0.5876, 0.2634) X_3605 = ISOGONAL CONJUGATE OF X(356) (0.5701, 0.2305) A B C X356 X1507 X1508 X358 X3279 X3605 (a, b, c) = (5, 6, 7) | AB = 1

X3605 (ISOGONAL CONJUGATE OF X356) 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 \(f(A,B,C) = 1/[\cos A/3 + 2 \cos B/3 \cos C/3]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.755109616049\)
▸ Incident Central Lines2 lines

{358, 3279}, {1507, 1508}

▸ Functional Relations1 relation

  • X3605 = orthology center of 1st Morley triangle and 1st Morley adjunct triangle