X3114

TgX(32)

X3114 = trilinear pole of line X669X804
< 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) { 32, 76 }: Central Line L(32, 76) { 183, 327 }: Central Line L(183, 327) { 264, 419 }: Central Line L(264, 419) { 6, 706 }: Central Line L(6, 706) { 313, 983 }: Central Line L(313, 983) { 870, 1215 }: Central Line L(870, 1215) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3117 = ISOGONAL CONJUGATE OF TgX(32) (0.6152, 0.2589) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_327 = ISOTOMIC CONJUGATE OF X(182) (0.5260, 0.2156) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_419 = -HIRST INVERSE OF X(25) (0.7266, 0.6950) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_706 = EVEN (- 4, 2) INFINITY POINT (0.0716, -0.1570) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_870 = ISOGONAL CONJUGATE OF X(869) (0.5328, 0.2015) X_1215 = ISOGONAL CONJUGATE OF X(1178) (0.5340, 0.2011) X_3114 = TgX(32) (0.5198, 0.2057) A B C X3117 X32 X76 X183 X327 X264 X419 X6 X706 X313 X983 X870 X1215 X3114 (a, b, c) = (5, 6, 7) | AB = 1

X3114 (TgX(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{3}(b^{4} + c^{4} + b^{2}c^{2})) : :\)
Search Value (6, 9, 13): \(3.070797265197\)
▸ Incident Central Lines6 lines

{6, 706}, {32, 76}, {183, 327}, {264, 419}, {313, 983}, {870, 1215}

▸ Functional Relations3 relations

Notes

Let A'B'C' be the 3rd Brocard triangle. Let La be the line through A' parallel to BC, and define Lb and Lc cyclically. Let A″ = Lb∩Lc, B″ = Lc∩La, C″ = La∩Lb. The lines AA″, BB″, CC″ concur in X3114. (Randy Hutson, August 29, 2018)