X₁₈₉₇

ZOSMA TRANSFORM OF X₁₀₅₄

X₁₈₉₇ = X₆₄₈-Ceva conjugate of X₁₇₈₃

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

X₁₈₉₇ (ZOSMA TRANSFORM OF X₁₀₅₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Derived Triangle: Anticomplementary Triangle △K_aK_bK_c — vertices K_a, K_b, K_c (Formed by lines through A, B, C parallel to opposite sides)

• Central Lines: {2, 2968}

• Related Centers: X₂ (CENTROID), X₂₉₆₈ (2nd MACBEATH POINT)

Trilinears: \((\sec A)/(b - c) : (\sec B)/(c - a) : (\sec C)/(a - b)\)

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

Search Value (6, 9, 13): \(-1.441183140962\)

▸ Incident Central Lines19 lines

{1, 318}, {4, 145}, {27, 295}, {29, 1807}, {33, 92}, {34, 1120}, {78, 1895}, {100, 108}, {101, 107}, {109, 522}, {112, 835}, {162, 190}, {192, 1013}, {243, 518}, {278, 1280}, {346, 1249}, {519, 1785}, {644, 1783}, {726, 1430}

▸ Functional Relations13 relations

• X₁₈₉₇ = isogonal conjugate of X₁₄₅₉

• X₁₈₉₇ = anticomplement of X₂₉₆₈

• X₁₈₉₇ = X₆₄₈-Ceva conjugate of X₁₇₈₃

• X₁₈₉₇ = cevapoint of X_i and X_j for these (i,j): (1, 522), (523, 1834), (650, 1864)

• X₁₈₉₇ = X₁₀₁-cross conjugate of X₁₉₀

• X₁₈₉₇ = crosspoint of X₆₄₈ and X₈₁₁

• X₁₈₉₇ = crosssum of X₆₄₇ and X₈₁₀

• X₁₈₉₇ = isotomic conjugate of X₄₀₂₅

• X₁₈₉₇ = trilinear pole of line X₄X₉ (complement of Soddy line, and Brocard axis of excentral triangle)

• X₁₈₉₇ = pole wrt polar circle of trilinear polar of X₅₁₄ (line X₁₁X₂₄₄, the Feuerbach tangent line)

• X₁₈₉₇ = polar conjugate of X₅₁₄

• X₁₈₉₇ = trilinear product X₄*X₁₀₀

• X₁₈₉₇ = trilinear product of circumcircle intercepts of line X₄X₈