X₂₁₉₁

X₂-ISOCONJUGATE OF X₂₁₈

X₂₁₉₁ = isogonal conjugate of X₃₈₇₀

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

X₂₁₉₁ (X₂-ISOCONJUGATE OF X₂₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 142}, {6, 354}

• Related Centers: X₃₈₇₀ (com[INVERSE(n(3rd EULER TRIANGLE))]), X₁ (INCENTER), X₁₄₂ (COMPLEMENT OF X₉), X₆ (SYMMEDIAN POINT), X₃₅₄ (WEILL POINT)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₂₁₈

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(-165.650233926789\)

▸ Incident Central Lines11 lines

{1, 142}, {6, 354}, {34, 1458}, {48, 1438}, {56, 1279}, {106, 1292}, {244, 1253}, {1027, 1459}, {1413, 1456}, {1419, 1421}, {2260, 2279}

▸ Functional Relations3 relations

• X₂₁₉₁ = isogonal conjugate of X₃₈₇₀

• X₂₁₉₁ = cevapoint of X_i and X_j for these (i,j): (244, 663), (1015, 2488)

• X₂₁₉₁ = X_i-cross conjugate of X_j for these (i,j): (41, 57), (2293, 6)