X₅₃₄

DIRECTION OF VECTOR AX + BX + CX, where X = X₁₉

X₅₃₄ = isogonal conjugate of X₃₈₈₈₃

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

X₅₃₄ (DIRECTION OF VECTOR AX + BX + CX, where X = X₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 19}, {30, 511}

• Related Centers: X₂ (CENTROID), X₁₉ (CLAWSON POINT), X₃₀ (EULER INFINITY POINT), X₅₁₁ (ISOGONAL CONJUGATE OF X₉₈)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = \tan A\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)

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

▸ Incident Central Lines4 lines

{2, 19}, {30, 511}, {553, 1407}, {1441, 1839}

▸ Functional Relations1 relation

• X₅₃₄ = isogonal conjugate of X₃₈₈₈₃