X₈₄₃

ISOGONAL CONJUGATE OF X₅₄₃

X₈₄₃ is the isogonal conjugate of X₅₄₃.

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

X₈₄₃ (ISOGONAL CONJUGATE OF X₅₄₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {352, 187}

• Related Centers: X₃₅₂ (INVERSE-IN-CIRCUMCIRCLE OF X₃₅₃), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X)

Trilinears: \(a/(2ax - by - cz) : :\), where \(x = x(a,b,c) = bc/(b^{2} - c^{2})\)

Search Value (6, 9, 13): \(5.067897888389\)

X₈₄₃ lies on the circumcircle.

▸ Incident Central Lines5 lines

{6, 691}, {99, 525}, {110, 187}, {111, 512}, {574, 805}

▸ Functional Relations15 relations

• X₈₄₃ = reflection of X₃₅₂ in X₁₈₇

• X₈₄₃ = isogonal conjugate of X₅₄₃

• X₈₄₃ = trilinear pole of line X₆X₃₅₁

• X₈₄₃ = Ψ(X₂, X₆₉₀)

• X₈₄₃ = Ψ(X₆, X₃₅₁)

• X₈₄₃ = circumcircle-antipode of X₂₇₀₉

• X₈₄₃ = reflection of X₂₇₀₉ in X₃

• X₈₄₃ = reflection of X₁₁₁ in the Brocard axis

• X₈₄₃ = inverse-in-circle-O(15,16) of X₁₁₀

• X₈₄₃ = 2nd-Parry-to-ABC similarity image of X₃₅₂

• X₈₄₃ = 3rd-Parry-to-circumsymmedial similarity image of X₁₁₁

• X₈₄₃ = X₉₁₄₄-of-4th-anti-Brocard-triangle

• X₈₄₃ = cevapoint of Schoute circle intercepts with Lemoine axis

• X₈₄₃ = X₆₉₁-of-circumsymmedial-triangle

• X₈₄₃ = barycentric product of circumcircle intercepts of line X₂X₆₉₀