X₃₅₀₈

INTERSECTION OF LINES X₁X_6 AND X₇₆X_1423

X₃₅₀₈ = X₃₈₅-Ceva conjugate of X₃₅₀₇

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

X₃₅₀₈ (INTERSECTION OF LINES X₁X_6 AND X₇₆X_1423) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {98, 813}

• Related Centers: X₃₈₅ (-HIRST INVERSE OF X₆), X₃₅₀₇ (INTERSECTION OF LINES X), X₁ (INCENTER), X₆ (SYMMEDIAN POINT), X₉₈ (TARRY POINT), X₈₁₃ (o-(- 1, 1) CIRCUMCIRCLE POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(a^{2} + bc)(b^{2} + bc + c^{2}) - (b + c)(b^{2}c^{2} + a^{2}b^{2} + a^{2}c^{2}) (E\). Danneels)

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

Search Value (6, 9, 13): \(-9.462368480657\)

X₃₅₀₈ lies on the cubic Z(X₃₈₅).

▸ Incident Central Lines10 lines

{1, 6}, {32, 983}, {76, 1423}, {98, 813}, {190, 1966}, {256, 1500}, {385, 3512}, {694, 3510}, {1018, 1756}, {1334, 1655}

▸ Functional Relations1 relation

• X₃₅₀₈ = X₃₈₅-Ceva conjugate of X₃₅₀₇