X2118

POINT KEPLER VII

< 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, 365 }: Central Line L(6, 365) { 238, 2119 }: Central Line L(238, 2119) { 2108, 2147 }: Central Line L(2108, 2147) { 2111, 2146 }: Central Line L(2111, 2146) 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_365 = SQUARE ROOT POINT (0.5864, 0.2502) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_2119 = -ISOCONJUGATE OF X(2118) (1.0031, 0.0103) X_2108 = POINT KEPLER I (-0.3883, 0.6500) X_2147 = -ISOCONJUGATE OF X(2146) (-0.1236, 0.7736) X_2111 = -ISOCONJUGATE OF X(2110) (-0.1997, 0.7497) X_2146 = -CEVA CONJUGATE OF X(365) (-0.3206, 0.6940) X_2118 = POINT KEPLER VII (1.6762, 1.6136) A B C X6 X365 X238 X2119 X2108 X2147 X2111 X2146 X2118 (a, b, c) = (5, 6, 7) | AB = 1

X2118 (POINT KEPLER VII) 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 \(f(a,b,c) = a(a + b + c)(bc)^{1/2} + (bc + ca + ab)[a - (ab)^{1/2} - (ac)^{1/2}]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-4.025763325476\)
▸ Incident Central Lines4 lines

{6, 365}, {238, 2119}, {2108, 2147}, {2111, 2146}