X₂₇₆

ISOGONAL CONJUGATE OF X₂₁₇

X₂₇₆ is the isogonal conjugate of X₂₁₇.

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

X₂₇₆ (ISOGONAL CONJUGATE OF X₂₁₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 95}, {76, 275}

• Related Centers: X₂₁₇ (-CEVA CONJUGATE OF X₅₁), X₃ (CIRCUMCENTER), X₉₅ (CEVAPOINT OF CENTROID AND CIRCUMCENTER), X₇₆ (3rd BROCARD POINT), X₂₇₅ (CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT)

Trilinears: \(\csc^{3} A \sec A \sec(B - C) : \csc^{3} B \sec B \sec(C - A) : \csc^{3} C \sec C \sec(A - B)\)

Barycentrics: \(\csc^{2} A \sec A \sec(B - C) : \csc^{2} B \sec B \sec(C - A) : \csc^{2} C \sec C \sec(A - B)\)

Search Value (6, 9, 13): \(160.227757913962\)

▸ Incident Central Lines5 lines

{3, 95}, {4, 327}, {54, 290}, {76, 275}, {97, 401}

▸ Functional Relations11 relations

• X₂₇₆ = isogonal conjugate of X₂₁₇

• X₂₇₆ = isotomic conjugate of X₂₁₆

• X₂₇₆ = cevapoint of X_i and X_j for these (i,j): (2, 264), (95, 275)

• X₂₇₆ = X_i-cross conjugate of X_j for these (i,j): (2, 95), (401, 290)

• X₂₇₆ = trilinear pole of line X₂₁₆X₆₄₇

• X₂₇₆ = inverse-in-Kiepert-hyperbola of X₁₉₈₉

• X₂₇₆ = {X₁₃,X₁₄}-harmonic conjugate of X₁₉₈₉

• X₂₇₆ = X₉₂-isoconjugate of X₅₀

• X₂₇₆ = Hofstadter -2 point

• X₂₇₆ = trilinear pole of line X₃₄₀X₅₂₀ (the isotomic conjugate of the Johnson circumconic, and the polar of X₅₁ wrt polar circle)

• X₂₇₆ = polar conjugate of X₅₁