X₁₈₂₄

ZOSMA TRANSFORM OF X₂

X₁₈₂₄ = intersection of tangents to hyperbola {{A, B, C,X₄,X₁₉}} at X₄ and X₁₉

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

X₁₈₂₄ (ZOSMA TRANSFORM OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 8}, {19, 25}

• Related Centers: X₁₄₄₄ (-BETH CONJUGATE OF X₃₃₂), X₄ (ORTHOCENTER), X₈ (NAGEL POINT), X₁₉ (CLAWSON POINT), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES)

Trilinears: \((b + c)\tan A : (c + a) \tan B : (a + b) \tan C\)

Barycentrics: \(a(b + c) \tan A : b(c + a) \tan B : c(a + b) \tan C\)

Search Value (6, 9, 13): \(-2.773750218836\)

▸ Incident Central Lines28 lines

{4, 8}, {10, 429}, {12, 431}, {19, 25}, {27, 295}, {28, 1255}, {34, 1887}, {42, 1880}, {51, 1864}, {65, 225}, {209, 1865}, {210, 430}, {213, 607}, {240, 444}, {278, 1002}, {427, 1848}, {428, 528}, {518, 1889}, {674, 1839}, {756, 862}, {851, 1214}, {942, 1068}, {989, 1039}, {990, 1473}, {1593, 1753}, {1726, 1754}, {1730, 1736}, {1785, 1894}

▸ Functional Relations11 relations

• X₁₈₂₄ = isogonal conjugate of X₁₄₄₄

• X₁₈₂₄ = complement of X₂₀₂₄₃

• X₁₈₂₄ = X_i-Ceva conjugate of X_j for these (i,j): (4, 1826), (33, 42), (225, 1826)

• X₁₈₂₄ = X_i-cross conjugate of X_j for these (i,j): (181, 42), (213, 37)

• X₁₈₂₄ = crosspoint of X_i and X_j for these (i,j): (4, 19), (33, 1857), (65, 1903), (225, 1826)

• X₁₈₂₄ = crosssum of X_i and X_j for these (i,j): (3, 63), (21, 1817), (77, 1804), (283, 1790)

• X₁₈₂₄ = intersection of tangents to hyperbola {{A, B, C,X₄,X₁₉}} at X₄ and X₁₉

• X₁₈₂₄ = pole wrt polar circle of trilinear polar of X₂₇₄ (line X₃₂₀X₃₅₀)

• X₁₈₂₄ = polar conjugate of X₂₇₄

• X₁₈₂₄ = barycentric product of vertices of 2nd extouch triangle

• X₁₈₂₄ = X₁₇₄-of-orthic-triangle if ABC is acute