X₃₆₆₂

2nd KIRIKAMI-MOSES POINT

X₃₆₆₂ = 3(\(a^{2}\) + \(b^{2}\) + \(c^{2})\)*X₂ + (\(a^{2}\) + \(b^{2}\) + \(c^{2}\) -2bc - 2ca - 2ab)X₇

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

X₃₆₆₂ (2nd KIRIKAMI-MOSES POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 7}, {75, 141}

• Related Centers: X₂ (CENTROID), X₇ (GERGONNE POINT), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₁₄₁ (COMPLEMENT OF SYMMEDIAN POINT)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b^{2} + c^{2} - bc)\)

Barycentrics: \(b^{2} + c^{2} - bc : c^{2} + a^{2} - ca : a^{2} + b^{2} - ab\)

Search Value (6, 9, 13): \(3.248043802486\)

▸ Incident Central Lines15 lines

{1, 2896}, {2, 7}, {6, 320}, {8, 1738}, {69, 239}, {75, 141}, {85, 257}, {86, 1333}, {273, 297}, {306, 3210}, {319, 599}, {614, 1716}, {982, 2887}, {1266, 1278}, {2345, 3619}

▸ Functional Relations9 relations

• X₃₆₆₂ = 3(\(a^{2}\) + \(b^{2}\) + \(c^{2})\)*X₂ + (\(a^{2}\) + \(b^{2}\) + \(c^{2}\) -2bc - 2ca - 2ab)X₇

• X₃₆₆₂ = (\(a^{2}\) + \(b^{2}\) + \(c^{2}\) - bc - ca - ab)X₇ + (\(a^{2}\) + \(b^{2}\) + \(c^{2})\)*X(9

• X₃₆₆₂ = (bc + ca + ab)*X₇₅ - 2(\(a^{2}\) + \(b^{2}\) + \(c^{2})\)X₁₄₁

• X₃₆₆₂ = anticomplement of X₁₇₃₅₃

• X₃₆₆₂ = isotomic conjugate of X₁₇₇₄₃

• X₃₆₆₂ = complement of X₁₇₃₅₀

• X₃₆₆₂ = {X₇₅,X₁₄₁}-harmonic conjugate of X₃₆₆₁

• X₃₆₆₂ = {X₅₉₄,X₁₇₂₂₈}-harmonic conjugate of X₃₆₆₁

• X₃₆₆₂ = {X₁₀₈₆,X₁₇₂₂₇}-harmonic conjugate of X₃₆₆₁