X3277

CENTER OF 3rd MORLEY TRIANGLE

X3277 = isogonal conjugate of X3607
< 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) { 356, 1134 }: Central Line L(356, 1134) { 1136, 1137 }: Central Line L(1136, 1137) { 3272, 3275 }: Central Line L(3272, 3275) { 3, 3282 }: Central Line L(3, 3282) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3607 = ISOGONAL CONJUGATE OF X(3277) (0.6128, 0.3358) X_356 = MORLEY CENTER (0.5727, 0.2361) X_1134 = 3rd MORLEY-TAYLOR-MARR CENTER (0.5584, 0.2154) X_1136 = 5th MORLEY-TAYLOR-MARR CENTER (0.6158, 0.4039) X_1137 = 6th MORLEY-TAYLOR-MARR CENTER (0.4890, 0.0964) X_3272 = CENTER OF EQUILATERAL TRIANGLE J1J2J3 (0.5698, 0.2349) X_3275 = PERSPECTOR OF TRIANGLES S1S2S3 AND J1J2J3 (0.6086, 0.2928) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3282 = PERSPECTOR OF TRIANGLES S1S2S3 AND T1T2T3 (0.5037, 0.1206) X_3277 = CENTER OF 3rd MORLEY TRIANGLE (0.5081, 0.1427) A B C X3607 X356 X1134 X1136 X1137 X3272 X3275 X3 X3282 X3277 (a, b, c) = (5, 6, 7) | AB = 1

X3277 (CENTER OF 3rd MORLEY TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos(A/3 - 4\pi /3) + 2 \cos(B/3 - 4\pi /3)\cos(C/3 - 4\pi /3)\)
Search Value (6, 9, 13): \(4.518040166177\)
▸ Linear Combinations1 combination
▸ Incident Central Lines4 lines

{3, 3282}, {356, 1134}, {1136, 1137}, {3272, 3275}

▸ Functional Relations1 relation