X₉₁₅

ISOGONAL CONJUGATE OF X₉₁₂

X₉₁₅ is the isogonal conjugate of X₉₁₂.

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

X₉₁₅ (ISOGONAL CONJUGATE OF X₉₁₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {34, 46}, {19, 101}

• Related Centers: X₅₁₇ (ISOGONAL CONJUGATE OF X₁₀₄), X₄ (ORTHOCENTER), X₃₄ (-BETH CONJUGATE OF X₄), X₄₆ (-CEVA CONJUGATE OF X₁), X₁₉ (CLAWSON POINT), X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT))

Trilinears: \((\tan A)/(\sin B (-1 + \cos A + \cos B) + \sin C (-1 + \cos A + \cos C)) : :\)

Barycentrics: \(a/((a^{2} - b^{2} - c^{2}) (a^{3} (b + c) - a^{2} (b^{2} + c^{2}) - a (b - c)^{2} (b + c) + (b^{2} - c^{2})^{2})) : :\)

Search Value (6, 9, 13): \(12.538665284115\)

X₉₁₅ lies on the circumcircle.

▸ Incident Central Lines7 lines

{19, 101}, {21, 925}, {24, 108}, {28, 110}, {34, 46}, {99, 286}, {242, 929}

▸ Functional Relations9 relations

• X₉₁₅ = isogonal conjugate of X₉₁₂

• X₉₁₅ = X₅₁₇-cross conjugate of X₄

• X₉₁₅ = antipode of X₄ in hyperbola {A, B, C,X₄,X₁₉}}

• X₉₁₅ = inverse-in-polar-circle of X₁₁₉

• X₉₁₅ = trilinear pole of line X₆X₃₆₅₇

• X₉₁₅ = Ψ(X₆, X₃₆₅₇)

• X₉₁₅ = polar conjugate of isogonal conjugate of X₃₂₆₅₅

• X₉₁₅ = polar conjugate of isotomic conjugate of X₂₉₉₀

• X₉₁₅ = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {A, B, C,X₄,X₁₉}}