X1976

TRILINEAR POLE OF PU(39)

X1976 = crosssum of X2 and X147
< 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, 98 }: Central Line L(2, 98) { 6, 157 }: Central Line L(6, 157) { 32, 263 }: Central Line L(32, 263) { 51, 251 }: Central Line L(51, 251) { 290, 308 }: Central Line L(290, 308) { 37, 692 }: Central Line L(37, 692) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_1976 = TRILINEAR POLE OF PU(39) (1.0272, -0.3962) A B C X325 X2 X98 X6 X157 X32 X263 X51 X251 X290 X308 X37 X692 X1976 (a, b, c) = (5, 6, 7) | AB = 1

X1976 (TRILINEAR POLE OF PU(39)) 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 \(f(a,b,c) = a^{2}/(a^{2}\cos B \cos C - bc \cos^{2} A)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.624431308222\)
▸ Incident Central Lines13 lines

{2, 98}, {6, 157}, {25, 1501}, {32, 263}, {37, 692}, {51, 251}, {111, 1495}, {237, 694}, {290, 308}, {351, 878}, {419, 685}, {879, 1177}, {1492, 1821}

▸ Functional Relations8 relations