X₇₉₈

CROSSDIFFERENCE OF X₁ AND X₇₅

X₇₉₈ = X₁₆₃-Ceva conjugate of X₃₁

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

X₇₉₈ (CROSSDIFFERENCE OF X₁ AND X₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 513}, {667, 788}

• Related Centers: X₇₉₉ (ISOGONAL CONJUGATE OF X₇₉₈), X₄₄ (-LINE CONJUGATE OF X₁), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀), X₆₆₇ (CROSSDIFFERENCE OF X₂ AND X₃₇), X₇₈₈ (ODD (- 3, 0) INFINITY POINT)

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

Barycentrics: \(a^{3}(b^{2} - c^{2}) : :\)

Search Value (6, 9, 13): \(7.168537293119\)

▸ Alternate Coordinates2 forms

• Trilinears: \(S_{B}\)\(S_{B}\) - \(S_{C}\)\(S_{C}\) : :

• Trilinears: \(\operatorname{area}(BCP(1)) - \operatorname{area}(BCU(1)) : :\)

▸ Incident Central Lines5 lines

{44, 513}, {163, 1101}, {667, 788}, {688, 872}, {765, 813}

▸ Functional Relations16 relations

• X₇₉₈ = isogonal conjugate of X₇₉₉

• X₇₉₈ = isotomic conjugate of X₄₆₀₂

• X₇₉₈ = complement of X₁₇₂₁₇

• X₇₉₈ = X₁₆₃-Ceva conjugate of X₃₁

• X₇₉₈ = crosspoint of X₃₁ and X₁₆₃

• X₇₉₈ = crosssum of X_i and X_j for these (i,j): (1, 798), (38, 661), (86, 1019), (99, 645), (190, 668), (513, 1107)

• X₇₉₈ = crossdifference of every pair of points on line X₁X₇₅

• X₇₉₈ = bicentric difference of PU(i) for i in (36, 85)

• X₇₉₈ = PU(36)-harmonic conjugate of X₁₉₆₄

• X₇₉₈ = PU(85)-harmonic conjugate of X₂₆₆₇

• X₇₉₈ = perspector wrt excentral triangle of the bianticevian conic of X₁ and X₂

• X₇₉₈ = X₆-isoconjugate of X₆₇₀

• X₇₉₈ = trilinear product of PU(105)

• X₇₉₈ = X₂-Ceva conjugate of X₃₈₉₈₆

• X₇₉₈ = perspector of hyperbola {A, B, C,X₁,X₃₁}}

• X₇₉₈ = trilinear pole of line X₃₁₂₁X₄₁₁₇ (the tangent to the inellipse that is the trilinear square of the Lemoine axis, at the trilinear square of X₅₁₂)