X₁₈₂₉

ZOSMA TRANSFORM OF X₁₀

X₁₈₂₉ = X₁₇₇-of-orthic triangle if ABC is acute

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

X₁₈₂₉ (ZOSMA TRANSFORM OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1902, 4}

• Related Centers: X₁₉₀₂ (ZOSMA TRANSFORM OF X₁₂₁₀), X₄ (ORTHOCENTER)

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X₁₀

Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X₁₀

Search Value (6, 9, 13): \(-2.112127610952\)

▸ Incident Central Lines34 lines

{1, 25}, {4, 8}, {6, 19}, {10, 427}, {24, 1385}, {27, 239}, {28, 60}, {29, 242}, {40, 1593}, {52, 912}, {56, 1452}, {57, 1398}, {209, 1869}, {225, 1866}, {235, 946}, {278, 959}, {388, 1892}, {392, 406}, {407, 1838}, {428, 519}, {429, 960}, {444, 1193}, {468, 1125}, {516, 1885}, {518, 1843}, {580, 1782}, {1100, 1474}, {1395, 1468}, {1482, 1598}, {1724, 1726}, {1825, 1877}, {1831, 1842}, {1852, 1858}, {1861, 1883}

▸ Functional Relations10 relations

• X₁₈₂₉ = reflection of X₁₉₀₂ in X₄

• X₁₈₂₉ = isogonal conjugate of X₁₇₉₁

• X₁₈₂₉ = anticomplement of X₃₇₆₁₃

• X₁₈₂₉ = X_i-Ceva conjugate of X_j for these (i,j): (4, 429), (19, 444)

• X₁₈₂₉ = crosspoint of X_i and X_j for these (i,j): (4, 28), (278, 286))

• X₁₈₂₉ = crosssum of X_i and X_j for these (i,j): (3, 72), (37, 197), (219, 228)

• X₁₈₂₉ = inverse-in-Fuhrmann-circle of X₅₀₉₀

• X₁₈₂₉ = X₁₇₇-of-orthic triangle if ABC is acute

• X₁₈₂₉ = polar conjugate of X₃₀₇₁₀

• X₁₈₂₉ = X₁-of-anti-Ara-triangle