X₃₂₂₉

ISOGONAL CONJUGATE OF X₃₂₂₅

X₃₂₂₉ is the isogonal conjugate of X₃₂₂₅.

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

X₃₂₂₉ (ISOGONAL CONJUGATE OF X₃₂₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 39}, {187, 237}

• Related Centers: X₃₂₂₅ (SS(a → bc) OF X₉₈), X₂ (CENTROID), X₃₉ (BROCARD MIDPOINT), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₂₃₇ (-LINE CONJUGATE OF X₂)

Trilinears: \(a(a^{2}b^{4} + a^{2}c^{4} - b^{2}c^{4} - c ^{2}b^{4}) : :\)

Search Value (6, 9, 13): \(-3.331548001177\)

▸ Incident Central Lines8 lines

{1, 893}, {2, 39}, {32, 1613}, {141, 706}, {187, 237}, {232, 420}, {511, 694}, {32746, 32747}

▸ Functional Relations11 relations

• X₃₂₂₉ = isogonal conjugate of X₃₂₂₅

• X₃₂₂₉ = isotomic conjugate of the isogonal conjugate of X₃₂₇₄₈

• X₃₂₂₉ = X_i-Ceva conjugate of X_j for these (i,j): (385, 511), (699, 6)

• X₃₂₂₉ = crosspoint of X_i and X_j for these (i,j): (2, 694), (6, 699)

• X₃₂₂₉ = crosssum of X_i and X_j for these (i,j): (2, 698), (6, 385), (192, 2238), (523, 2086)

• X₃₂₂₉ = crossdifference of every pair of points on the line X₂X₆₆₉

• X₃₂₂₉ = complement of X₃₉₇₈

• X₃₂₂₉ = crossdifference of PU(148)

• X₃₂₂₉ = X₂-Ceva conjugate of X₃₉₀₈₀

• X₃₂₂₉ = perspector of hyperbola {{A, B, C,X₆,X₆₇₀,X₂₅₄₂₄}}

• X₃₂₂₉ = intersection of line X₂X₃₉[X₁₉₄] and line through X₂-Ceva conjugate of X₁₉₄ and X₁₉₄-Ceva conjugate of X₂