X₂₈₀₆

ISOGONAL CONJUGATE OF X₂₇₂₂

X₂₈₀₆ is the isogonal conjugate of X₂₇₂₂.

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

X₂₈₀₆ (ISOGONAL CONJUGATE OF X₂₇₂₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {11, 127}, {100, 112}

• Related Centers: X₂₇₂₂ (SR(X₁₀₀, X₁₁₂)), X₁₁ (FEUERBACH POINT), X₁₂₇ (-OF-MEDIAL-TRIANGLE), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₁₁₂ (Ψ(ORTHOCENTER, SYMMEDIAN POINT))

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X₂₇₂₂

Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)

▸ Incident Central Lines5 lines

{11, 127}, {30, 511}, {100, 112}, {104, 1297}, {119, 132}

▸ Functional Relations1 relation

• X₂₈₀₆ = isogonal conjugate of X₂₇₂₂

Notes

Let I_a be the reflection of X₁ in the perpendicular bisector of BC, and define I_b and I_c cyclically. X₂₈₀₆ = X₅₂₅-of-I_aI_bI_c; I_aI_bI_c is the inner Garcia triangle. (Randy Hutson, February 10, 2016)