X₃₈₂₄

X₃₆₇₁com(3rd EULER TRIANGLE)

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

X₃₈₂₄ (X₃₆₇₁com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {5, 142}, {30, 1125}

• Related Centers: X₅ (NINE-POINT CENTER), X₁₄₂ (COMPLEMENT OF X₉), X₃₀ (EULER INFINITY POINT), X₁₁₂₅ (COMPLEMENT OF X₁₀)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (a + 2b + 2c)(b^{3} + c^{3} - a^{2}b - a^{2}c - 2abc - b^{2}c - bc^{2})\)

Search Value (6, 9, 13): \(2.075959673006\)

▸ Incident Central Lines7 lines

{5, 142}, {30, 1125}, {79, 3683}, {442, 942}, {527, 3634}, {1698, 3715}, {3454, 3739}