X3643

X14 OF 1st BROCARD TRIANGLE

X3643 = 1st-Brocard-isogonal conjugate of X22689
< 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, 13 }: Central Line L(2, 13) { 14, 76 }: Central Line L(14, 76) { 30, 141 }: Central Line L(30, 141) { 15, 299 }: Central Line L(15, 299) { 32, 396 }: Central Line L(32, 396) { 6, 532 }: Central Line L(6, 532) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_396 = MIDPOINT OF X(13) AND X(15) (0.5699, 0.2349) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_532 = DIRECTION OF VECTOR AX + BX + CX, where X = X(17) (0.8927, 0.6671) X_3643 = OF 1st BROCARD TRIANGLE (0.4888, 0.1210) A B C X2 X13 X14 X76 X30 X141 X15 X299 X32 X396 X6 X532 X3643 (a, b, c) = (5, 6, 7) | AB = 1

X3643 (X14 OF 1st BROCARD TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(-2 \sqrt{3} (a^{4}+2 b^{2} c^{2}) S+a^{6}-(b^{2}+c^{2}) a^{4}+2 (b^{4}+3 b^{2} c^{2}+c^{4}) a^{2}-2 (b^{4}-c^{4}) \cdot (b^{2}-c^{2}) : :\)
Search Value (6, 9, 13): \(4.637963307397\)
▸ Incident Central Lines17 lines

{2, 13}, {3, 619}, {4, 635}, {6, 532}, {14, 76}, {15, 299}, {18, 627}, {30, 141}, {32, 396}, {61, 634}, {69, 533}, {381, 623}, {531, 599}, {617, 2896}, {629, 1656}, {630, 631}, {2925, 3132}

▸ Functional Relations1 relation

  • X3643 = 1st-Brocard-isogonal conjugate of X22689