X₁₈₉₆

ZOSMA TRANSFORM OF X₁₀₄₇

X₁₈₉₆ = X₄-cross conjugate of X₂₉

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

X₁₈₉₆ (ZOSMA TRANSFORM OF X₁₀₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 29}, {4, 51}

• Related Centers: X₄ (ORTHOCENTER), X₂₉ (CEVAPOINT OF INCENTER AND ORTHOCENTER), X₁ (INCENTER), X₅₁ (CENTROID OF ORTHIC TRIANGLE)

Trilinears: \((\sec A)/(\sec B + \sec C) : (\sec B)/(\sec C + \sec A) : (\sec C)/(\sec A + \sec B)\)

Barycentrics: \((\tan A)/(\sec B + \sec C) : (\tan B)/(\sec C + \sec A) : (\tan C)/(\sec A + \sec B)\)

Search Value (6, 9, 13): \(2.038254379740\)

▸ Alternate Coordinates1 form

• Trilinears: \((\sec^{2} A)(b + c - a)/(b + c) : (\sec^{2} B)(c + a - b)/(c + a) : (\sec^{2} C)(a + b - c)/(a + b)\)

▸ Incident Central Lines11 lines

{1, 29}, {4, 51}, {7, 286}, {8, 1857}, {9, 318}, {21, 243}, {27, 84}, {28, 104}, {393, 941}, {412, 1715}, {823, 1156}

▸ Functional Relations6 relations

• X₁₈₉₆ = cevapoint of X_i and X_j for these (i,j): (1, 1715), (4, 158)

• X₁₈₉₆ = X₄-cross conjugate of X₂₉

• X₁₈₉₆ = isogonal conjugate of X₂₂₃₄₁

• X₁₈₉₆ = pole wrt polar circle of trilinear polar of X₁₂₁₄ (line X₅₂₀X₆₅₆)

• X₁₈₉₆ = polar conjugate of X₁₂₁₄

• X₁₈₉₆ = X₆₃-isoconjugate of X₁₄₀₉