X₂₀₈₈

PK-TRANSFORM OF X₁₁₀

X₂₀₈₈ = isogonal conjugate of X₃₉₂₉₅

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

X₂₀₈₈ (PK-TRANSFORM OF X₁₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {115, 125}

• Related Centers: X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₁₁₅ (CENTER OF KIEPERT HYPERBOLA), X₁₂₅ (CENTER OF JERABEK HYPERBOLA)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{2} - c^{2})^{2}[(b^{2} + c^{2} - a^{2})^{2} - b^{2}c^{2}]\)

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

Search Value (6, 9, 13): \(3.181583690078\)

▸ Incident Central Lines2 lines

{3, 6}, {115, 125}

▸ Functional Relations5 relations

• X₂₀₈₈ = isogonal conjugate of X₃₉₂₉₅

• X₂₀₈₈ = X_i-Ceva conjugate of X_j for these (i,j): (50, 2081), (74, 512), (94, 523), (323, 526)

• X₂₀₈₈ = crosspoint of X_i and X_j for these (i,j): (94, 523), (323, 526)

• X₂₀₈₈ = crosssum of X_i and X_j for these (i,j): (50, 110), (112, 403), (476, 1989)

• X₂₀₈₈ = Brocard-circle-inverse of X₃₂₇₆₁