X3276

CENTER OF 2nd MORLEY TRIANGLE

X3276 = isogonal conjugate of X3606
< 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, 357 }: Central Line L(356, 357) { 1136, 1137 }: Central Line L(1136, 1137) { 3272, 3274 }: Central Line L(3272, 3274) { 3, 3280 }: Central Line L(3, 3280) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3606 = ISOGONAL CONJUGATE OF X(3276) (0.5988, 0.8316) X_356 = MORLEY CENTER (0.5727, 0.2361) X_357 = 1st MORLEY-TAYLOR-MARR CENTER (0.5757, 0.2422) 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_3274 = PERSPECTOR OF TRIANGLES P1P2P3 AND J1J2J3 (0.5554, 0.2055) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3280 = PERSPECTOR OF TRIANGLES P1P2P3 AND T1T2T3 (0.5240, 0.1540) X_3276 = CENTER OF 2nd MORLEY TRIANGLE (0.4192, -0.0726) A B C X3606 X356 X357 X1136 X1137 X3272 X3274 X3 X3280 X3276 (a, b, c) = (5, 6, 7) | AB = 1

X3276 (CENTER OF 2nd MORLEY TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos(A/3 - 2\pi /3) + 2 \cos(B/3 - 2\pi /3) \cos(C/3 - 2\pi /3) : :\)
Search Value (6, 9, 13): \(14.203661952053\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(\cos(A/3) - \cos(B/3) \cos(C/3) : :\)

  • Trilinears: \(\sec(A/3) - \sec(B/3) \sec(C/3) : :\)

▸ Linear Combinations1 combination
▸ Incident Central Lines4 lines

{3, 3280}, {356, 357}, {1136, 1137}, {3272, 3274}

▸ Functional Relations1 relation