X₂₃₆₀

X₂-ISOCONJUGATE OF X₁₉₀₃

X₂₃₆₀ = X₂₁-Ceva conjugate of X₅₈

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₃₆₀ (X₂-ISOCONJUGATE OF X₁₉₀₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 19}, {3, 64}

• Related Centers: X₁ (INCENTER), X₁₉ (CLAWSON POINT), X₃ (CIRCUMCENTER), X₆₄ (ISOGONAL CONJUGATE OF X₂₀)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₉₀₃

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(-4.140422610846\)

▸ Incident Central Lines23 lines

{1, 19}, {3, 64}, {21, 84}, {25, 581}, {27, 946}, {29, 515}, {36, 1780}, {40, 1817}, {56, 58}, {72, 101}, {73, 2299}, {102, 110}, {184, 580}, {208, 223}, {405, 572}, {595, 2352}, {604, 1453}, {662, 1043}, {1191, 1333}, {1201, 2206}, {1203, 2260}, {1214, 1782}, {1728, 2261}

▸ Functional Relations6 relations

• X₂₃₆₀ = isogonal conjugate of X₃₉₁₃₀

• X₂₃₆₀ = crossdifference of every pair of points on line X₆₅₆X₃₇₀₀

• X₂₃₆₀ = X₂₁-Ceva conjugate of X₅₈

• X₂₃₆₀ = cevapoint of X_i and X_j for these (i,j): (221, 7114), (48, 154), (198, 2187)

• X₂₃₆₀ = X₁₉₈-cross conjugate of X₁₈₁₇

• X₂₃₆₀ = trilinear product X_i*X_j for these {i,j}: {3, 3194}, {6, 1817}, {21, 221}, {28, 7078}, {29, 7114}, {31, 8822}, {34, 1819}, {40, 58}, {60, 227}, {81, 198}, {86, 2187}, {110, 6129}, {163, 14837}, {196, 2193}, {208, 283}, {223, 284}, {322, 2206}, {329, 1333}, {333, 2199}, {347, 2194}, {593, 21871}, {604, 27398}, {849, 21075}, {859, 15501}, {1014, 7074}, {1172, 7011}, {1408, 7080}, {1412, 2324}, {1437, 7952}, {1444, 3195}, {1576, 17896}, {1790, 2331}, {1812, 3209}, {2287, 6611}, {2299, 7013}, {4565, 14298}

Notes

See Dasari Naga Vijay Krishna, On a Conic Through Twelve Notable Points, Int. J. Adv. Math. and Mech. 7(2) (2019) 1-15.