X₃₁₈₃

X₂₀-CEVA CONJUGATE OF X₄

X₃₁₈₃ = X₂₀-Ceva conjugate of X₄

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

X₃₁₈₃ (X₂₀-CEVA CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3346, 3}

• Related Centers: X₃₃₄₆ (ISOGONAL CONJUGATE OF X₁₄₉₈), X₃ (CIRCUMCENTER)

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X₂₀ and \(u : v : w\) = X₄

Search Value (6, 9, 13): \(3.763721050575\)

X₃₁₈₃ lies on the Darboux cubic.

▸ Incident Central Lines12 lines

{1, 196}, {3, 1033}, {4, 64}, {19, 84}, {20, 3348}, {40, 1712}, {376, 1075}, {393, 1192}, {1490, 3354}, {1498, 2131}, {1620, 1990}, {3182, 3473}

▸ Functional Relations7 relations

• X₃₁₈₃ = reflection of X₃₃₄₆ in X₃

• X₃₁₈₃ = anticomplement of X₃₃₅₄₆

• X₃₁₈₃ = X₂₀-Ceva conjugate of X₄

• X₃₁₈₃ = crosspoint of X₂₀ and X₂₀₆₀

• X₃₁₈₃ = isogonal conjugate of X₃₃₄₈

• X₃₁₈₃ = orthocenter of cevian triangle of X₂₀

• X₃₁₈₃ = perspector of hexyl triangle and anticevian triangle of X₁₇₁₂