X₃₈₀

INTERSECTION OF LINES X₁X_19 AND X₉X_55

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

X₃₈₀ (INTERSECTION OF LINES X₁X_19 AND X₉X_55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 19}, {6, 40}

• Related Centers: X₁ (INCENTER), X₁₉ (CLAWSON POINT), X₆ (SYMMEDIAN POINT), X₄₀ (BEVAN POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a)[3a^{3} + (b + c)(3a^{2} + (b - c)^{2} + a(b + c))]\)

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

Search Value (6, 9, 13): \(2.331057740835\)

▸ Incident Central Lines7 lines

{1, 19}, {6, 40}, {9, 55}, {165, 579}, {223, 608}, {281, 950}, {282, 1036}