X₂₂₄

X₇-CEVA CONJUGATE OF X₆₃

X₂₂₄ = X₇-Ceva conjugate of X₆₃

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

X₂₂₄ (X₇-CEVA CONJUGATE OF X₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 63}, {21, 90}

• Related Centers: X₇ (GERGONNE POINT), X₆₃ (ISOGONAL CONJUGATE OF X₁₉), X₃ (CIRCUMCENTER), X₂₁ (SCHIFFLER POINT), X₉₀ (-CROSS CONJUGATE OF X₁)

Trilinears: \([\cot B \cos^{2}(B/2) + \cot C \cos^{2}(C/2) - \cot A \cos^{2}(A/2)]\cot A\)

Search Value (6, 9, 13): \(4.002542176200\)

▸ Alternate Coordinates1 form

• Trilinears: \((b^{2} + c^{2} - a^{2}) (a^{4} - b^{4} - c^{4} - 2 a^{3} (b + c) - 2 a^{2} b c + 2 a (b^{3} + c^{3}) + 2 b^{2} c^{2}) : :\)

▸ Incident Central Lines7 lines

{1, 377}, {3, 63}, {8, 914}, {21, 90}, {46, 100}, {65, 1004}, {908, 1079}

▸ Functional Relations3 relations

• X₂₂₄ = X₇-Ceva conjugate of X₆₃

• X₂₂₄ = barycentric product of vertices of Gemini triangle 7

• X₂₂₄ = barycentric product of vertices of Gemini triangle 8