X₅₅₈

(X₁,X₅₇)-ANSWER TO QUESTION A

X₅₅₈ = X₂-Ceva conjugate of X₃₉₁₂₂

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

X₅₅₈ ((X₁,X₅₇)-ANSWER TO QUESTION A) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 178}

• Related Centers: X₂ (CENTROID), X₁₇₈ (2nd MID-ARC POINT)

Trilinears: \(\sec A/2 \tan A/4 : \sec B/2 \tan B/4 : \sec C/2 \tan C/4\)

Barycentrics: \(\sin^{2}(A/4) : \sin^{2}(B/4) : \sin^{2}(C/4)\)

Search Value (6, 9, 13): \(0.301523843514\)

▸ Alternate Coordinates1 form

• Trilinears: \(\csc A (1 - \cos A/2) : :\)

▸ Incident Central Lines1 line

{2, 178}

▸ Functional Relations1 relation

• X₅₅₈ = X₂-Ceva conjugate of X₃₉₁₂₂