X₂₀₉₈

REFLECTION OF X₅₆ IN X₁

X₂₀₉₈ is the reflection of X₅₆ in X₁.

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

X₂₀₉₈ (REFLECTION OF X₅₆ IN X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {56, 1}

• Related Centers: X₅₆ (EXSIMILICENTER), X₁ (INCENTER)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a)(a^{2} - 2b^{2} - 2c^{2} + 4bc - ab - ac)\)

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

Search Value (6, 9, 13): \(3.193497995727\)

▸ Incident Central Lines12 lines

{1, 3}, {8, 11}, {21, 1392}, {33, 1828}, {145, 497}, {219, 1731}, {499, 1387}, {519, 1837}, {944, 1317}, {952, 1479}, {1000, 1389}, {1108, 1732}

▸ Functional Relations8 relations

• X₂₀₉₈ = reflection of X_i in X_j for these (i,j): (8, 1329), (56, 1)

• X₂₀₉₈ = crosssum of X₁ and X₁₄₂₀

• X₂₀₉₈ = {X₁,X₄₀}-harmonic conjugate of X₁₃₁₉

• X₂₀₉₈ = homothetic center of intangents triangle and reflection of tangential triangle in X₁

• X₂₀₉₈ = homothetic center of Mandart-incircle triangle and 5th mixtilinear triangle

• X₂₀₉₈ = X₅₆-of-Mandart-incircle-triangle

• X₂₀₉₈ = X₅₆-of-5th-mixtilinear-triangle

• X₂₀₉₈ = Ursa-major-to-Ursa-minor similarity image of X₈