X₂₃₇₄

CIR(X₆₉)

X₂₃₇₄ = cevapoint of X₂₅ and X₄₆₈

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

X₂₃₇₄ (CIR(X₆₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {25, 99}, {4, 126}

• Related Centers: X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₄₆₈ (-LINE CONJUGATE OF X₃), X₉₉ (STEINER POINT), X₄ (ORTHOCENTER), X₁₂₆ (-OF-MEDIAL-TRIANGLE)

Trilinears: \(F(u,v,w) : F(v,w,u) : F(w,u,v)\), where F is as indicated just before X₂₃₆₅, and \(u : v : w\) = X₆₉.

Barycentrics: \(aF(u,v,w) : bF(v,w,u) : cF(w,u,v)\)

Search Value (6, 9, 13): \(2.709227325227\)

X₂₃₇₄ lies on the circumcircle.

▸ Incident Central Lines6 lines

{4, 126}, {25, 99}, {110, 193}, {112, 459}, {468, 691}, {925, 1995}

▸ Functional Relations9 relations

• X₂₃₇₄ = cevapoint of X₂₅ and X₄₆₈

• X₂₃₇₄ = X₅₂₄-cross conjugate of X₄

• X₂₃₇₄ = isogonal conjugate of X₈₆₈₁

• X₂₃₇₄ = Λ(X₆, X₁₁₉₆)

• X₂₃₇₄ = Ψ(X₆, X₃₅₆₆)

• X₂₃₇₄ = inverse-in-polar-circle of X₁₂₆

• X₂₃₇₄ = trilinear pole of line X₆X₃₅₆₆

• X₂₃₇₄ = polar conjugate of anticomplement of X₆₃₉₀

• X₂₃₇₄ = X₆₃-isoconjugate of X₃₂₉₁