X2668

CROSSSUM OF PU(85)

< 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, 6 }: Centroid–Symmedian Line { 42, 873 }: Central Line L(42, 873) { 171, 1509 }: Central Line L(171, 1509) { 1403, 1434 }: Central Line L(1403, 1434) { 799, 2107 }: Central Line L(799, 2107) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_873 = ISOGONAL CONJUGATE OF X(872) (0.5339, 0.2011) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_1509 = ISOGONAL CONJUGATE OF X(1500) (0.5682, 0.2347) X_1403 = -BETH CONJUGATE OF X(43) (0.6606, 0.3972) X_1434 = -BETH CONJUGATE OF X(274) (0.6014, 0.2949) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_2107 = -ISOCONJUGATE OF X(2106) (1.0304, 0.0996) X_2668 = CROSSSUM OF PU(85) (0.5612, 0.2256) A B C X2 X6 X42 X873 X171 X1509 X1403 X1434 X799 X2107 X2668 (a, b, c) = (5, 6, 7) | AB = 1

X2668 (CROSSSUM OF PU(85)) 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 \(f(a,b,c) = a^{2}bc/[(a + b)(a + c)] + [bc/(b + c)]^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.969787788421\)
▸ Incident Central Lines5 lines

{2, 6}, {42, 873}, {171, 1509}, {799, 2107}, {1403, 1434}