X₃₇₃₇

X₆₅₆com(HEXYL TRIANGLE)

X₃₇₃₇ = crosssum of Kiepert hyperbola intercepts of antiorthic axis

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

X₃₇₃₇ (X₆₅₆com(HEXYL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {59, 110}, {36, 238}

• Related Centers: X₅₉ (ISOGONAL CONJUGATE OF X₁₁), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₃₆ (INVERSE-IN-CIRCUMCIRCLE OF INCENTER), X₂₃₈ (-LINE CONJUGATE OF X₃₇)

Trilinears: \((b - c)(b + c - a)/(b + c) : :\)

Barycentrics: \(a(b - c)(b + c - a)/(b + c) : :\)

Search Value (6, 9, 13): \(-13.108514971299\)

▸ Alternate Coordinates3 forms

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

• Trilinears: \(\tan(B/2 - C/2) : :\)

• Trilinears: \(\tan(B' - C') : :\), where J_aJ_bJ_c = excentral triangle

▸ Incident Central Lines16 lines

{1, 523}, {9, 3287}, {36, 238}, {54, 2616}, {59, 110}, {86, 1027}, {112, 2728}, {242, 514}, {284, 1024}, {512, 2959}, {521, 650}, {522, 663}, {741, 2726}, {759, 953}, {832, 1491}, {1443, 1447}

▸ Functional Relations3 relations

• X₃₇₃₇ = isogonal conjugate of X₄₅₅₁

• X₃₇₃₇ = crosssum of Kiepert hyperbola intercepts of antiorthic axis

• X₃₇₃₇ = SS(A → J_a) of X₂₆₁₆, where J_aJ_bJ_c is the excentral triangle