X₉₂₄

CROSSDIFFERENCE OF X₅ AND X₆

As the isogonal conjugate of a point on the circumcircle, X₉₂₄ lies on the line at infinity.

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

X₉₂₄ (CROSSDIFFERENCE OF X₅ AND X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {30, 511}, {50, 647}

• Related Centers: X₉₂₅ (ANTICOMPLEMENT OF X₁₃₆), X₃₀ (EULER INFINITY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈), X₅₀ (-CEVA CONJUGATE OF X₁₈₄), X₆₄₇ (CROSSDIFFERENCE OF X₂ AND X₃)

Trilinears: \(b \cos(A - B) - c \cos(A - C) : :\)

Barycentrics: \(\sec 2B - \sec 2C : :\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines4 lines

{30, 511}, {50, 647}, {66, 879}, {669, 684}

▸ Functional Relations10 relations

• X₉₂₄ = isogonal conjugate of X₉₂₅

• X₉₂₄ = isotomic conjugate of isogonal conjugate of X₃₄₉₅₂

• X₉₂₄ = complementary conjugate of X₁₃₆

• X₉₂₄ = X_i-Ceva conjugate of X_j for these (i,j): (2, 39013), (4, 136), (70, 125)

• X₉₂₄ = crosspoint of X_i and X_j for these (i,j): (4, 110), (99, 275)

• X₉₂₄ = crosssum of X_i and X_j for these (i,j): (3, 523), (216, 512)

• X₉₂₄ = crossdifference of every pair of points on line X₅X₆

• X₉₂₄ = perspector of hyperbola {A, B, C,X₂,X₂₄}}

• X₉₂₄ = intersection of trilinear polars of X₂ and X₂₄

• X₉₂₄ = barycentric square root of X₃₉₀₁₃