X₂₉₈₈

DC(X₁₀₂)

X₂₉₈₈ = cevapoint of X₆ and X₅₁₅

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

X₂₉₈₈ (DC(X₁₀₂)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {29, 110}, {92, 651}

• Related Centers: X₆ (SYMMEDIAN POINT), X₅₁₅ (ISOGONAL CONJUGATE OF X₁₀₂), X₂₉ (CEVAPOINT OF INCENTER AND ORTHOCENTER), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₉₂ (CEVAPOINT OF INCENTER AND CLAWSON POINT), X₆₅₁ (TRILINEAR POLE OF LINE X₁X₃)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X₂₉₇₉, using U = X₁₀₂

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(3.312811414688\)

X₂₉₈₈ lies on the MacBeath circumconic.

▸ Incident Central Lines5 lines

{2, 1813}, {8, 1331}, {29, 110}, {92, 651}, {312, 1332}

▸ Functional Relations5 relations

• X₂₉₈₈ = isogonal conjugate of X₈₆₀₇

• X₂₉₈₈ = cevapoint of X₆ and X₅₁₅

• X₂₉₈₈ = complement of anticomplementary conjugate of X₃₅₅₁₆

• X₂₉₈₈ = X₂₄₃₂-cross conjugate of X₁₃₀₉

• X₂₉₈₈ = trilinear pole of line X₃X₅₂₂