X₃₁₄₉

X₂₈₅-CEVA CONJUGATE OF X₁

X₃₁₄₉ = X₂₈₅-Ceva conjugate of X₁

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

X₃₁₄₉ (X₂₈₅-CEVA CONJUGATE OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {1, 227}

• Related Centers: X₂₈₅ (-CROSS CONJUGATE OF X₂₁), X₁ (INCENTER), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₂₂₇ (-CEVA CONJUGATE OF X₆₅)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂₈₅ and \(u : v : w\) = X₁

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)

Search Value (6, 9, 13): \(-9.354547766682\)

▸ Incident Central Lines28 lines

{1, 227}, {2, 3}, {35, 1699}, {40, 936}, {55, 946}, {56, 515}, {57, 1071}, {64, 1715}, {78, 517}, {84, 1728}, {100, 962}, {221, 1771}, {222, 1745}, {282, 2270}, {355, 956}, {573, 1437}, {578, 1437}, {581, 940}, {603, 2635}, {908, 1259}, {938, 944}, {971, 1445}, {1155, 1158}, {1454, 1858}, {1498, 1754}, {1617, 3086}, {1735, 1854}, {1741, 1903}

▸ Functional Relations2 relations

• X₃₁₄₉ = X₂₈₅-Ceva conjugate of X₁

• X₃₁₄₉ = X₂₁-gimel conjugate of X₃

Notes

As a point on the Euler line, X₃₁₄₉ has Shinagawa coefficients \((\$aS_{A}\$ - abc, -\$aS_{A}\$ - abc)\).