X2146

X238-CEVA CONJUGATE OF X365

X2146 = X238-Ceva conjugate of X365
< 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) { 292, 365 }: Central Line L(292, 365) { 1, 2119 }: Central Line L(1, 2119) { 2111, 2118 }: Central Line L(2111, 2118) { 238, 2147 }: Central Line L(238, 2147) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_365 = SQUARE ROOT POINT (0.5864, 0.2502) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_1 = INCENTER (0.5714, 0.2333) X_2119 = -ISOCONJUGATE OF X(2118) (1.0031, 0.0103) X_2111 = -ISOCONJUGATE OF X(2110) (-0.1997, 0.7497) X_2118 = POINT KEPLER VII (1.6762, 1.6136) X_2147 = -ISOCONJUGATE OF X(2146) (-0.1236, 0.7736) X_2146 = -CEVA CONJUGATE OF X(365) (-0.3206, 0.6940) A B C X238 X365 X292 X1 X2119 X2111 X2118 X2147 X2146 (a, b, c) = (5, 6, 7) | AB = 1

X2146 (X238-CEVA CONJUGATE OF X365) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{1/2}(b^{1/2}/v + c^{1/2}/w - a^{1/2}/u) : b^{1/2}(c^{1/2}/w + a^{1/2}/u - b^{1/2}/v) : c^{1/2}(a^{1/2}/u + b^{1/2}/v - c^{1/2}/w)\), where u : v : \(w = a^{2} - bc : b^{2} - ca : c^{2} - ab\)
Barycentrics: \(a^{3/2}(b^{1/2}/v + c^{1/2}/w - a^{1/2}/u) : b^{3/2}(c^{1/2}/w + a^{1/2}/u - b^{1/2}/v) : c^{3/2}(a^{1/2}/u + b^{1/2}/v - c^{1/2}/w)\)
Search Value (6, 9, 13): \(3.773193386785\)

X2146 lies on the 2nd equal-areas cubic (K155).

▸ Incident Central Lines4 lines

{1, 2119}, {238, 2147}, {292, 365}, {2111, 2118}

▸ Functional Relations1 relation