X2549

EXSIMILICENTER(MOSES CIRCLE, (X4,2R))

The circle (X4,2R) is identified at X2474.
< 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) { 6, 30 }: Central Line L(6, 30) { 4, 39 }: Central Line L(4, 39) { 20, 32 }: Central Line L(20, 32) { 2, 99 }: Central Line L(2, 99) { 3, 230 }: Central Line L(3, 230) { 194, 315 }: Central Line L(194, 315) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_4 = ORTHOCENTER (0.6122, 0.3958) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2 = CENTROID (0.5374, 0.2000) X_99 = STEINER POINT (0.1109, 0.4322) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_2549 = EXSIMILICENTER(MOSES CIRCLE, (X(4),2R)) (0.5679, 0.1833) A B C X6 X30 X4 X39 X20 X32 X2 X99 X3 X230 X194 X315 X2549 (a, b, c) = (5, 6, 7) | AB = 1

X2549 (EXSIMILICENTER(MOSES CIRCLE, (X4,2R))) 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 \(f(A,B,C) = 2 \cos B \cos C - \sin(A + \omega ) \csc \omega\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.357675494111\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a): g(c,a,b)\), where \(g(a,b,c) = bc(a^{4} - b^{4} - c^{4} - 2a^{2}b^{2} - 2a^{2}c^{2} + 2b^{2}c^{2})\) (Eric Danneels, Nov. 11, 2004)

▸ Incident Central Lines29 lines

{2, 99}, {3, 230}, {4, 39}, {6, 30}, {10, 1571}, {20, 32}, {53, 1597}, {69, 538}, {147, 1569}, {184, 1562}, {187, 376}, {193, 754}, {194, 315}, {388, 1500}, {497, 1515}, {516, 1572}, {625, 1007}, {1194, 1370}, {1478, 2276}, {1479, 2275}, {1504, 1587}, {1505, 1588}, {1573, 2550}, {1574, 2551}, {1885, 2207}, {2033, 2542}, {2034, 2543}, {2035, 2546}, {2036, 2547}

▸ Functional Relations5 relations