X₆₁₀

X₆₃-CEVA CONJUGATE OF X₁

X₆₁₀ = X₆₃-Ceva conjugate of X₁

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

X₆₁₀ (X₆₃-CEVA CONJUGATE OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 9}, {1, 19}

• Related Centers: X₆₃ (ISOGONAL CONJUGATE OF X₁₉), X₁ (INCENTER), X₃ (CIRCUMCENTER), X₉ (MITTENPUNKT), X₁₉ (CLAWSON POINT)

Trilinears: \(\operatorname{area} - a^{2} \cot A : \operatorname{area} - b^{2} \cot B : \operatorname{area} - c^{2}\cot C\)

Barycentrics: \(a(\operatorname{area} - a^{2} \cot A) : b(\operatorname{area} - b^{2} \cot B) : c(\operatorname{area} - c^{2} \cot C)\)

Search Value (6, 9, 13): \(-6.409966276989\)

▸ Alternate Coordinates3 forms

• Trilinears: \(\tan B + \tan C - \tan A : \tan C + \tan A - \tan B : \tan A + \tan B - \tan C\) (Randy Hutson, 9/23/2011)

• Trilinears: \(S_{B}S_{C} - a^{2}S_{A} : :\) (C. Lozada, 9/07/2013)

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

▸ Incident Central Lines9 lines

{1, 19}, {3, 9}, {6, 57}, {40, 219}, {71, 165}, {159, 197}, {169, 572}, {281, 515}, {326, 662}

▸ Functional Relations4 relations

• X₆₁₀ = isogonal conjugate of X₂₁₈₄

• X₆₁₀ = X₆₃-Ceva conjugate of X₁

• X₆₁₀ = X₂₀₄-cross conjugate of X₁

• X₆₁₀ = X₂₁₆₅-of-excentral-triangle