X₂₃₇₃

CIR(X₆₇)

X₂₃₇₃ = anticomplement of X₁₅₆₀

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

X₂₃₇₃ (CIR(X₆₇)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 112}, {22, 99}

• Related Centers: X₂₃₉₃ (ISOGONAL CONJUGATE OF X₂₃₇₃), X₂ (CENTROID), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT)), X₂₂ (EXETER POINT), X₉₉ (STEINER POINT)

Trilinears: \(F(u,v,w) : F(v,w,u) : F(w,u,v)\), where F is as indicated just before X₂₃₆₅, and \(u : v : w\) = X₆₇.

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

Search Value (6, 9, 13): \(13.854895742712\)

X₂₃₇₃ lies on the circumcircle.

▸ Incident Central Lines17 lines

{2, 112}, {20, 1296}, {22, 99}, {23, 935}, {25, 339}, {69, 110}, {95, 933}, {101, 306}, {107, 264}, {108, 1441}, {109, 307}, {183, 1302}, {253, 1301}, {316, 691}, {328, 476}, {827, 1799}, {1304, 1494}

▸ Functional Relations11 relations

• X₂₃₇₃ = isogonal conjugate of X₂₃₉₃

• X₂₃₇₃ = isotomic conjugate of X₈₅₈

• X₂₃₇₃ = anticomplement of X₁₅₆₀

• X₂₃₇₃ = cevapoint of X_i and X_j for these (i,j): (2, 23), (3, 524), (669, 1648)

• X₂₃₇₃ = X_i-cross conjugate of X_j for these (i,j): (67, 671), (468, 2)

• X₂₃₇₃ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {{A, B, C,X₂,X₆₉}}

• X₂₃₇₃ = trilinear pole of line X₆X₅₂₅

• X₂₃₇₃ = trilinear pole, wrt circummedial triangle, of line X₂₂X₁₈₃

• X₂₃₇₃ = Ψ(X₆, X₅₂₅)

• X₂₃₇₃ = orthoptic-circle-of-Steiner-inellipse-inverse of X₁₂₇

• X₂₃₇₃ = orthoptic-circle-of-Steiner-circumellipse-inverse of X₁₃₂₁₉