X₃₂₃₀

ISOGONAL CONJUGATE OF X₃₂₂₇

X₃₂₃₀ is the isogonal conjugate of X₃₂₂₇.

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

X₃₂₃₀ (ISOGONAL CONJUGATE OF X₃₂₂₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3125, 3290}

• Related Centers: X₃₁₂₅ (DANNEELS PERSPECTOR FOR X₈₁), X₃₂₉₀ (INTERSECTION OF LINES X)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(2bc - ab - ac)\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(-2.365272465953\)

▸ Incident Central Lines21 lines

{1, 6}, {31, 2242}, {39, 1201}, {41, 2241}, {99, 2106}, {101, 1914}, {106, 292}, {111, 2703}, {172, 595}, {187, 237}, {239, 1016}, {519, 2238}, {672, 1015}, {739, 898}, {869, 2177}, {992, 2321}, {995, 2276}, {1018, 1575}, {1125, 2295}, {1193, 1500}, {1197, 1621}

▸ Functional Relations11 relations

• X₃₂₃₀ = reflection of X₃₁₂₅ in X₃₂₉₀

• X₃₂₃₀ = isogonal conjugate of X₃₂₂₇

• X₃₂₃₀ = X_i-Ceva conjugate of X_j for these (i,j): (739, 6), (898, 667)

• X₃₂₃₀ = crosspoint of X_i and X_j for these (i,j): (6, 739), (898, 1016)

• X₃₂₃₀ = crosssum of X_i and X_j for these (i,j): (2, 536), (513, 1646), (891, 1015)

• X₃₂₃₀ = crossdifference of every pair of points on the line X₂X₅₁₃

• X₃₂₃₀ = bicentric sum of PU(26)

• X₃₂₃₀ = complement of anticomplementary conjugate of X₃₉₃₆₀

• X₃₂₃₀ = perspector of hyperbola {{A, B, C,X₆,X₁₀₀}}

• X₃₂₃₀ = PU(26)-harmonic conjugate of X₆₆₇

• X₃₂₃₀ = inverse-in-Parry-isodynamic-circle of X₅₀₄₀; see X₂

Notes

X₃₂₃₀ is the point of intersection of the line X₁X₆ and the trilinear polar of X₆; c.f. X₁₃₂₃. (Randy Hutson, February 10, 2016)