X₃₇₇₈

X₁₉₆₄com[INVERSE(nT(-bc, b²))]

X₃₇₇₈ = isogonal conjugate of isotomic conjugate of X₂₈₈₇

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

X₃₇₇₈ (X₁₉₆₄com[INVERSE(nT(-bc, b²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {42, 181}, {142, 244}

• Related Centers: X₂₈₈₇ (COMPLEMENTARY CONJUGATE OF X₃₇), X₄₂ (CROSSPOINT OF INCENTER AND SYMMEDIAN POINT), X₁₈₁ (APOLLONIUS POINT), X₁₄₂ (COMPLEMENT OF X₉), X₂₄₄ (-LINE CONJUGATE OF X₁₀₀)

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

Search Value (6, 9, 13): \(1.804370031698\)

▸ Incident Central Lines26 lines

{6, 560}, {10, 3728}, {31, 579}, {37, 3122}, {39, 2309}, {42, 181}, {63, 1716}, {71, 3747}, {75, 700}, {141, 2228}, {142, 244}, {209, 3725}, {256, 291}, {313, 714}, {573, 2209}, {674, 1964}, {723, 789}, {749, 751}, {869, 2277}, {982, 2887}, {1445, 1758}, {1918, 2245}, {2085, 3670}, {2275, 3056}, {3009, 3688}, {3123, 3663}

▸ Functional Relations1 relation

• X₃₇₇₈ = isogonal conjugate of isotomic conjugate of X₂₈₈₇