X₁₇₆₉

MIMOSA TRANSFORM OF X₉₀₁

X₁₇₆₉ = trilinear product of circumcircle intercepts of Sherman line

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

X₁₇₆₉ (MIMOSA TRANSFORM OF X₉₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {104, 106}, {108, 109}

• Related Centers: X₁₆₂ (CEVAPOINT OF X₁₀₈ AND X₁₀₉), X₁₈₄₅ (ZOSMA TRANSFORM OF X₈₀), X₁₀₄ (ANTIPODE OF X₁₀₀), X₁₀₆ (Λ(INCENTER, CENTROID)), X₁₀₈ (Ψ(CIRCUMCENTER, INCENTER)), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER))

Trilinears: - (cos A)/x + (cos B)/y + (cos C)/z,\(x : y : z\) = X₉₀₁

Search Value (6, 9, 13): \(-2.771186059722\)

▸ Alternate Coordinates1 form

• Trilinears: \((b - c) (a^{2} (b + c) - 2 a b c - (b - c)^{2} (b + c)) : :\)

▸ Incident Central Lines5 lines

{11, 244}, {104, 106}, {108, 109}, {240, 522}, {513, 663}

▸ Functional Relations6 relations

• X₁₇₆₉ = isogonal conjugate of X₃₆₀₃₇

• X₁₇₆₉ = X₁₆₂-Ceva conjugate of X₁₈₄₅

• X₁₇₆₉ = crosspoint of X_i and X_j for these (i,j): (88, 934), (162, 759)

• X₁₇₆₉ = crosssum of X_i and X_j for these (i,j): (31, 1635), (522, 1737), (656, 758)

• X₁₇₆₉ = trilinear product of circumcircle intercepts of Sherman line

• X₁₇₆₉ = crossdifference of every pair of points on line X₉X₄₈ (the Fermat axis of the excentral triangle and of the 2nd extouch triangle)