X₂₆₁₈

DIFFERENCE OF PU(72)

X₂₆₁₈ = X₁-Ceva conjugate of X₂₆₁₆

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

X₂₆₁₈ (DIFFERENCE OF PU(72)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {12, 523}, {240, 522}

• Related Centers: X₁ (INCENTER), X₂₆₁₆ (POINT TANIA), X₁₂ ({X), X₅₂₃ (ISOGONAL CONJUGATE OF X₁₁₀), X₂₄₀ (-LINE CONJUGATE OF X₄₈), X₅₂₂ (ISOGONAL CONJUGATE OF X₁₀₉)

Trilinears: \(\tan(C - A) - \tan(B - A) : :\)

Search Value (6, 9, 13): \(1.515600317338\)

▸ Alternate Coordinates3 forms

• Trilinears: \(\sin(2B - 2C) : :\)

• Trilinears: \((\csc 2A)(\cot 2B - \cot 2C) : :\)

• Trilinears: \((\sec 2A)(\tan 2B - \tan 2C) : :\)

▸ Incident Central Lines6 lines

{1, 2616}, {12, 523}, {240, 522}, {823, 2633}, {1101, 2625}, {2290, 2622}

▸ Functional Relations6 relations

• X₂₆₁₈ = isogonal conjugate of X₃₆₁₃₄

• X₂₆₁₈ = X₁-Ceva conjugate of X₂₆₁₆

• X₂₆₁₈ = crosspoint of X₁ and X₂₆₁₇

• X₂₆₁₈ = crosssum of X₁ and X₂₆₁₆

• X₂₆₁₈ = crossdifference of every pair of points on line X₄₇X₄₈

• X₂₆₁₈ = perspector of anticevian triangle of X₄₈ and tangential triangle, wrt anticevian triangle of X₄₇, of bianticevian conic of X₁ and X₄₇