X2547

EXSIMILICENTER(1st LEMOINE 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) { 4, 83 }: Central Line L(4, 83) { 2, 1342 }: Central Line L(2, 1342) { 20, 1343 }: Central Line L(20, 1343) { 10, 1700 }: Central Line L(10, 1700) { 194, 1670 }: Central Line L(194, 1670) { 388, 1672 }: Central Line L(388, 1672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_2 = CENTROID (0.5374, 0.2000) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X(1342) (0.4118, -0.0436) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_2547 = EXSIMILICENTER(1st LEMOINE CIRCLE, (X(4),2R)) (0.5254, 0.1011) A B C X4 X83 X2 X1342 X20 X1343 X10 X1700 X194 X1670 X388 X1672 X2547 (a, b, c) = (5, 6, 7) | AB = 1

X2547 (EXSIMILICENTER(1st LEMOINE 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 \(f(A,B,C) = \cos B \cos C - \cos(A - \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.306594428106\)
▸ Incident Central Lines18 lines

{2, 1342}, {4, 83}, {10, 1700}, {20, 1343}, {194, 1670}, {371, 2544}, {372, 2545}, {388, 1672}, {497, 1673}, {516, 1701}, {1587, 1687}, {1588, 1688}, {1680, 2550}, {1681, 2551}, {2035, 2548}, {2036, 2549}, {2471, 2552}, {2472, 2553}