X₁₈₂₆

ZOSMA TRANSFORM OF X₆

X₁₈₂₆ = cevapoint of X₁ and X₁₇₁₉

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

X₁₈₂₆ (ZOSMA TRANSFORM OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 9}, {12, 37}

• Related Centers: X₁₇₉₀ (INVERSE MIMOSA TRANSFORM OF X₆), X₄ (ORTHOCENTER), X₉ (MITTENPUNKT), X₁₂ ({X), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID)

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X₆

Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X₆

Search Value (6, 9, 13): \(-25.003915317345\)

▸ Incident Central Lines26 lines

{4, 9}, {6, 1837}, {11, 1108}, {12, 37}, {25, 1631}, {27, 1268}, {28, 1224}, {29, 1220}, {33, 42}, {48, 515}, {53, 1904}, {65, 1868}, {80, 1172}, {92, 264}, {101, 1300}, {209, 1859}, {210, 430}, {219, 355}, {286, 334}, {407, 1213}, {427, 1841}, {579, 1737}, {608, 1877}, {857, 1441}, {1744, 1770}, {1836, 1853}

▸ Functional Relations8 relations

• X₁₈₂₆ = isogonal conjugate of X₁₇₉₀

• X₁₈₂₆ = X_i-Ceva conjugate of X_j for these (i,j): (4, 1824), (281, 37)

• X₁₈₂₆ = cevapoint of X₁ and X₁₇₁₉

• X₁₈₂₆ = X₄₂-cross conjugate of X₁₀

• X₁₈₂₆ = crosspoint of X₄ and X₉₂

• X₁₈₂₆ = crosssum of X₃ and X₄₈

• X₁₈₂₆ = pole wrt polar circle of trilinear polar of X₈₆ (line X₂₃₉X₅₁₄)

• X₁₈₂₆ = polar conjugate of X₈₆