X₃₃₇₆

COT(A - π/3) POINT

X₃₃₇₆ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

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

X₃₃₇₆ (COT(A - π/3) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {14, 484}, {1, 1095}

• Related Centers: X₃₃₇₅ (TAN(A - π/3) POINT), X₁₄ (2nd ISOGONIC CENTER), X₄₈₄ (1st EVANS PERSPECTOR), X₁ (INCENTER), X₁₀₉₅ (TRILINEAR SQUARE OF X₁₆)

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = \cot(A - \pi /3)\)

Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)

Search Value (6, 9, 13): \(2.957648956498\)

▸ Incident Central Lines3 lines

{1, 1095}, {14, 484}, {19, 2166}

▸ Functional Relations2 relations

• X₃₃₇₆ = isogonal conjugate of X₃₃₇₅

• X₃₃₇₆ = trilinear product of X₁₄ and X₆₁