X3972

X3314com(3rd BROCARD TRIANGLE)

X3972 = perspector of ABC and circumsymmedial triangle of 1st Brocard triangle
< 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) { 3, 83 }: Central Line L(3, 83) { 6, 99 }: Central Line L(6, 99) { 32, 76 }: Central Line L(32, 76) { 2, 187 }: Central Line L(2, 187) { 112, 264 }: Central Line L(112, 264) { 251, 305 }: Central Line L(251, 305) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) 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_2 = CENTROID (0.5374, 0.2000) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_3972 = com(3rd BROCARD TRIANGLE) (0.5831, 0.2729) A B C X3 X83 X6 X99 X32 X76 X2 X187 X112 X264 X251 X305 X3972 (a, b, c) = (5, 6, 7) | AB = 1

X3972 (X3314com(3rd BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(2a^{4} + b^{2}c^{2} : 2b^{4} + c^{2}a^{2} : 2c^{4} + a^{2}b^{2}\)
Search Value (6, 9, 13): \(1.344425647019\)
▸ Incident Central Lines15 lines

{2, 187}, {3, 83}, {6, 99}, {32, 76}, {39, 3552}, {69, 1285}, {112, 264}, {183, 1384}, {251, 305}, {350, 609}, {376, 3618}, {574, 3329}, {691, 1316}, {754, 3314}, {1078, 3053}

▸ Functional Relations2 relations