X3734

X6com(1st BROCARD TRIANGLE)

Let A'B'C' be the 1st Brocard triangle. Let A″ be the trilinear pole, with respect to A'B'C', of line BC, and define B″ and C″ cyclically. The lines A'A″, B'B″, C'C″ concur in X3734.
< 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) { 2, 99 }: Central Line L(2, 99) { 32, 76 }: Central Line L(32, 76) { 30, 141 }: Central Line L(30, 141) { 83, 194 }: Central Line L(83, 194) { 183, 187 }: Central Line L(183, 187) { 6, 538 }: Central Line L(6, 538) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_99 = STEINER POINT (0.1109, 0.4322) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) X_3734 = com(1st BROCARD TRIANGLE) (0.5222, 0.2083) A B C X2 X99 X32 X76 X30 X141 X83 X194 X183 X187 X6 X538 X3734 (a, b, c) = (5, 6, 7) | AB = 1

X3734 (X6com(1st BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{4} + 2b^{2}c^{2}\)
Search Value (6, 9, 13): \(2.765215441678\)
▸ Incident Central Lines17 lines

{2, 99}, {4, 626}, {6, 538}, {30, 141}, {32, 76}, {39, 1975}, {69, 754}, {83, 194}, {182, 2782}, {183, 187}, {316, 3314}, {350, 2242}, {381, 625}, {1078, 3552}, {1235, 1968}, {1352, 2794}, {1909, 2241}

▸ Functional Relations7 relations