X₅₂₆

ISOGONAL CONJUGATE OF X₄₇₆

X₅₂₆ is the isogonal conjugate of X₄₇₆.

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

X₅₂₆ (ISOGONAL CONJUGATE OF X₄₇₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {110, 351}, {30, 511}

• Related Centers: X₄₇₆ (TIXIER POINT), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₃₅₁ (CENTER OF THE PARRY CIRCLE), X₃₀ (EULER INFINITY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈)

Trilinears: \((1 + 2 \cos 2A)\sin(B - C) : :\)

▸ Alternate Coordinates1 form

• Trilinears: a(b^2 - c^2)[(b^2 + c^2 - a^2)^2 - b^2c^2] : :, As the isogonal conjugate of a point on the circumcircle, X₅₂₆ lies on the line at infinity.

▸ Incident Central Lines10 lines

{6, 2492}, {30, 511}, {67, 879}, {110, 351}, {125, 3134}, {686, 2433}, {895, 2987}, {1177, 2435}, {1769, 2650}, {2611, 3024}

▸ Functional Relations20 relations

• X₅₂₆ = isogonal conjugate of X₄₇₆

• X₅₂₆ = isotomic conjugate of X₃₅₁₃₉

• X₅₂₆ = complementary conjugate of X₃₂₅₈

• X₅₂₆ = X₂-Ceva conjugate of X₁₈₃₃₄

• X₅₂₆ = X₁₁₀-Ceva conjugate of X₁₅₁₁

• X₅₂₆ = crosspoint of X₇₄ and X₁₁₀

• X₅₂₆ = crosssum of X₃₀ and X₅₂₃

• X₅₂₆ = crossdifference of every pair of points on line X₆X₁₃

• X₅₂₆ = X_i-isoconjugate of X_j for these (i,j): (49, 2166), (265, 2964)

• X₅₂₆ = perspector of hyperbola {A, B, C,X₂,X₁₅,X₁₆}}

• X₅₂₆ = intersection of trilinear polars of X₂, X₁₅, and X₁₆

• X₅₂₆ = trilinear pole of line of: X₂₀₈₈, tripolar centroid of X₁₅, tripolar centroid of X₁₆

• X₅₂₆ = X₅₂₃-of-orthocentroidal-triangle

• X₅₂₆ = X₅₂₃-of-X₄-Brocard-triangle

• X₅₂₆ = X₆₀₈₈-of-circumsymmedial-triangle

• X₅₂₆ = Thomson-isogonal conjugate of X₄₇₇

• X₅₂₆ = Lucas-isogonal conjugate of X₄₇₇

• X₅₂₆ = X₆-isoconjugate of X₃₂₆₈₀

• X₅₂₆ = X₉₂-isoconjugate of X₃₂₆₆₂

• X₅₂₆ = intersection of tangents to Walsmith rectangular hyperbola at PU(4)