X1915

CROSSSUM OF PU(11)

X1915 = polar conjugate of isotomic conjugate of X37893
< 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) { 6, 25 }: Central Line L(6, 25) { 31, 292 }: Central Line L(31, 292) { 110, 251 }: Central Line L(110, 251) { 2, 1501 }: Central Line L(2, 1501) { 32, 1613 }: Central Line L(32, 1613) { 141, 1799 }: Central Line L(141, 1799) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_2 = CENTROID (0.5374, 0.2000) X_1501 = TRILINEAR 5th POWER POINT (0.6596, 0.3922) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_1613 = TCC-PERSPECTOR OF X(31) (0.7015, 0.3763) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.4477, 0.0833) X_1915 = CROSSSUM OF PU(11) (0.6078, 0.3108) A B C X6 X25 X31 X292 X110 X251 X2 X1501 X32 X1613 X141 X1799 X1915 (a, b, c) = (5, 6, 7) | AB = 1

X1915 (CROSSSUM OF PU(11)) 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 \(f(a,b,c) = a(a^{4} + b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.618207362552\)
▸ Incident Central Lines6 lines

{2, 1501}, {6, 25}, {31, 292}, {32, 1613}, {110, 251}, {141, 1799}

▸ Functional Relations2 relations