X1922

TRILINEAR POLE OF PU(12)

X1922 = perspector of ABC and unary cofactor triangle of Gemini triangle 31
< 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) { 58, 101 }: Central Line L(58, 101) { 6, 291 }: Central Line L(6, 291) { 81, 335 }: Central Line L(81, 335) { 727, 813 }: Central Line L(727, 813) { 1416, 1428 }: Central Line L(1416, 1428) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1921 = CROSSDIFFERENCE OF PU(12) (-1.0027, -0.8795) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_1416 = -BETH CONJUGATE OF X(105) (1.0588, -0.1921) X_1428 = -BETH CONJUGATE OF X(238) (0.5173, 0.1103) X_1922 = TRILINEAR POLE OF PU(12) (0.9912, 0.0547) A B C X1921 X58 X101 X6 X291 X81 X335 X727 X813 X1416 X1428 X1922 (a, b, c) = (5, 6, 7) | AB = 1

X1922 (TRILINEAR POLE OF PU(12)) 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 \(f(a,b,c) = a^{3}/(a^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.052166640553\)
▸ Incident Central Lines5 lines

{6, 291}, {58, 101}, {81, 335}, {727, 813}, {1416, 1428}

▸ Functional Relations3 relations