X₇₆₅

CEVAPOINT OF X₁ AND X₁₀₀

X₇₆₅ is the cevapoint of X₁ and X₁₀₀.

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

X₇₆₅ (CEVAPOINT OF X₁ AND X₁₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {59, 518}, {100, 513}

• Related Centers: X₁ (INCENTER), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT), X₅₉ (ISOGONAL CONJUGATE OF X₁₁), X₅₁₈ (ISOGONAL CONJUGATE OF X₁₀₅), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀)

Trilinears: \((b - c) ^{-2} : (c - a) ^{-2} : (a - b) ^{-2}\)

Barycentrics: \(a(b - c) ^{-2} : b(c - a) ^{-2} : c(a - b) ^{-2}\)

Search Value (6, 9, 13): \(1.476717806338\)

▸ Incident Central Lines8 lines

{1, 1052}, {59, 518}, {100, 513}, {101, 898}, {109, 522}, {238, 519}, {660, 662}, {798, 813}

▸ Functional Relations7 relations

• X₇₆₅ = isogonal conjugate of X₂₄₄

• X₇₆₅ = isotomic conjugate of X₁₁₁₁

• X₇₆₅ = cevapoint of X_i and X_j for these (i,j): (1, 100), (31, 101)

• X₇₆₅ = X_i-cross conjugate of X_j for these (i,j): (1, 100), (9, 190), (31, 101)

• X₇₆₅ = crosssum of X₁ and X₁₀₅₂

• X₇₆₅ = crossdifference of every pair of points on line X₇₆₄X₂₀₈₇

• X₇₆₅ = trilinear pole of line X₁₀₀X₁₀₁ (the tangent at X₁₀₀ to the circumconic centered at X₉; also the locus of trilinear poles of tangents at P to hyperbola {A, B, C,X₁,P}}, as P moves on line X₁X₆)