X₂₁₉₃

X₂-ISOCONJUGATE OF X₂₂₅

X₂₁₉₃ = cevapoint of X₄₈ and X₅₇₇

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

X₂₁₉₃ (X₂-ISOCONJUGATE OF X₂₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {21, 270}

• Related Centers: X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₂₁ (SCHIFFLER POINT), X₂₇₀ (ISOGONAL CONJUGATE OF X₂₀₁)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₂₂₅

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

Search Value (6, 9, 13): \(4.020178422433\)

▸ Alternate Coordinates1 form

• Trilinears: \((\sin 2A) (\cos B + \cos C) : :\)

▸ Incident Central Lines19 lines

{1, 1744}, {3, 6}, {21, 270}, {30, 1865}, {48, 255}, {71, 906}, {81, 1214}, {112, 1295}, {212, 2289}, {219, 283}, {222, 1790}, {268, 2192}, {286, 448}, {859, 1474}, {1396, 1465}, {1444, 1814}, {1809, 2287}, {1880, 1950}, {2150, 2194}

▸ Functional Relations9 relations

• X₂₁₉₃ = complement of isotomic conjugate of X₁₈₁₂₃

• X₂₁₉₃ = X_i-Ceva conjugate of X_j for these (i,j): (21, 2194), (1790, 1437), (1798, 184)

• X₂₁₉₃ = cevapoint of X₄₈ and X₅₇₇

• X₂₁₉₃ = X_i-cross conjugate of X_j for these (i,j): (48, 284), (652, 906)

• X₂₁₉₃ = crosspoint of X_i and X_j for these (i,j): (21, 1812), (283, 1790)

• X₂₁₉₃ = crosssum of X_i and X_j for these (i,j): (1, 1744), (65, 1880), (225, 1826)

• X₂₁₉₃ = X₉₂-isoconjugate of X₆₅

• X₂₁₉₃ = X₁₀₈-isoconjugate of X₁₅₇₇

• X₂₁₉₃ = {X₁₈₀₅,X₁₈₀₆}-harmonic conjugate of X₃