X₃₉₂₈

X₁₅₄com[INVERSE(n(INTANGENTS TRIANGLE))]

X₃₉₂₈ = centroid of Gemini triangle 24

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

X₃₉₂₈ (X₁₅₄com[INVERSE(n(INTANGENTS TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 7}, {30, 84}

• Related Centers: X₂ (CENTROID), X₇ (GERGONNE POINT), X₃₀ (EULER INFINITY POINT), X₈₄ (ISOGONAL CONJUGATE OF X₄₀)

Trilinears: \(t(A,B,C) : t(B,C,A) : t(C,A,B)\), where \(t(A,B,C) = 3 \cot A - \csc A\) (Peter Moses, 1/13/2012)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(3a^{2} - 3b^{2} - 3c^{2} + 2bc)\)

Search Value (6, 9, 13): \(20.114671262539\)

▸ Incident Central Lines30 lines

{1, 3052}, {2, 7}, {30, 84}, {31, 3677}, {40, 376}, {46, 529}, {55, 3243}, {165, 518}, {191, 3338}, {200, 1155}, {219, 1407}, {222, 2323}, {528, 1768}, {536, 1764}, {551, 3333}, {614, 896}, {758, 3576}, {940, 3247}, {956, 2093}, {958, 3339}, {960, 3361}, {982, 1707}, {988, 1046}, {1449, 3666}, {1453, 3670}, {1697, 3241}, {1743, 3752}, {1761, 2257}, {2975, 3340}, {3359, 3654}

▸ Functional Relations3 relations

• X₃₉₂₈ = isogonal conjugate of isotomic conjugate of X₂₁₆₀₅

• X₃₉₂₈ = centroid of Gemini triangle 24

• X₃₉₂₈ = intouch-to-excentral similarity image of X₂