X₃₇₁₈

X₁₇₁₆com(EXTOUCH TRIANGLE)

X₃₇₁₈ = excentral-to-ABC barycentric image of X₁₇₁₆

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

X₃₇₁₈ (X₁₇₁₆com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {10, 75}, {69, 72}

• Related Centers: X₁₃₉₅ (-BETH CONJUGATE OF X₂₅), X₁₀ (SPIEKER CENTER), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₆₉ (SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE), X₇₂ (ISOGONAL CONJUGATE OF X₂₈)

Trilinears: \(\cot A \csc A \csc^{2}(A/2) : \cot B \csc B \csc^{2}(B/2) : \cot C \csc C \csc^{2}(C/2)\) (Peter Moses, 12/19/11)

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

Search Value (6, 9, 13): \(6.426604434433\)

▸ Incident Central Lines10 lines

{7, 3263}, {9, 312}, {10, 75}, {69, 72}, {78, 332}, {86, 975}, {190, 1760}, {305, 307}, {322, 668}, {740, 1716}

▸ Functional Relations3 relations

• X₃₇₁₈ = isogonal conjugate of X₁₃₉₅

• X₃₇₁₈ = isotomic conjugate of X₃₄

• X₃₇₁₈ = excentral-to-ABC barycentric image of X₁₇₁₆