X₃₅₉₅

ISOTOMIC CONJUGATE OF 2nd DIXIT POINT

X₃₅₉₅ is the isotomic conjugate of 2nd dixit point.

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

X₃₅₉₅ (ISOTOMIC CONJUGATE OF 2nd DIXIT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {4, 1164}

• Related Centers: X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₄ (ORTHOCENTER), X₁₁₆₄ (POINT ALTAIR)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b^{2} + c^{2} - a^{2} - 6 \operatorname{area}(ABC))\)

Barycentrics: \(2S_{A}\) - 3S : \(2S_{B}\) - 3S : \(2S_{C}\) - 3S [Conway notation]

Search Value (6, 9, 13): \(-4.058759072471\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (3 - 2 \cot A) \csc A\)

▸ Incident Central Lines6 lines

{2, 6}, {4, 1164}, {76, 3590}, {487, 3091}, {638, 3523}, {642, 1587}

▸ Functional Relations1 relation

• X₃₅₉₅ = {X₂,X₆₉}-harmonic conjugate of X₃₅₉₃