X₂₃₄₆

X₂-ISOCONJUGATE OF X₁₄₇₅

X₂₃₄₆ = isogonal conjugate of X₃₅₄

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

X₂₃₄₆ (X₂-ISOCONJUGATE OF X₁₄₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {7, 55}, {100, 142}

• Related Centers: X₁ (INCENTER), X₅₅ (INSIMILICENTER), X₇ (GERGONNE POINT), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₄₂ (COMPLEMENT OF X₉)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₁₄₇₅

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

Search Value (6, 9, 13): \(2.088190552631\)

▸ Alternate Coordinates1 form

• Trilinears: \(1/[(\sin B) \cot(B/2) + (\sin C) \cot(C/2)] : :\) (Randy Hutson, 9/23/2011)

▸ Incident Central Lines13 lines

{1, 1170}, {4, 390}, {7, 55}, {8, 344}, {9, 1174}, {21, 518}, {37, 294}, {79, 516}, {84, 1803}, {100, 142}, {523, 885}, {651, 2293}, {1014, 2223}

▸ Functional Relations6 relations

• X₂₃₄₆ = isogonal conjugate of X₃₅₄

• X₂₃₄₆ = cevapoint of X₁ and X₅₅

• X₂₃₄₆ = X_i-cross conjugate of X_j for these (i,j): (514, 100), (657, 651), (1174, 1170)

• X₂₃₄₆ = crosssum of X_i and X_j for these (i,j): (2, 57), (9, 145)

• X₂₃₄₆ = perspector of ABC and triangle formed by orthic axes of BIC, CIA, AIB

• X₂₃₄₆ = perspector of ABC and cross-triangle of ABC and Honsberger triangle