X₃₃₈

CEVAPOINT OF X₁₁₅ AND X₁₂₅

X₃₃₈ is the cevapoint of X₁₁₅ and X₁₂₅.

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

X₃₃₈ (CEVAPOINT OF X₁₁₅ AND X₁₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 67}, {2, 94}

• Related Centers: X₁₁₅ (CENTER OF KIEPERT HYPERBOLA), X₁₂₅ (CENTER OF JERABEK HYPERBOLA), X₄ (ORTHOCENTER), X₆₇ (ISOGONAL CONJUGATE OF X₂₃), X₂ (CENTROID), X₉₄ (ISOGONAL CONJUGATE OF X₅₀)

Trilinears: \((b^{2} - c^{2})^{2}/a^{3} : (c^{2} - a^{2})^{2}/b^{3} : (a^{2} - b^{2})^{2}/c^{3}\)

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

Search Value (6, 9, 13): \(3.809002144110\)

▸ Alternate Coordinates2 forms

• Trilinears: \(\csc A \sin^{2}(B - C) : \csc B \sin^{2}(C - A) : \csc C \sin^{2}(A - B)\)

• Barycentrics: \(\sin^{2}(B - C) : \sin^{2}(C - A) : \sin^{2}(A - B)\)

X₃₃₈ lies on the inconic with perspector X₂₀₅₂.

▸ Incident Central Lines8 lines

{2, 94}, {4, 67}, {6, 264}, {50, 401}, {76, 599}, {115, 127}, {125, 136}, {141, 311}

▸ Functional Relations9 relations

• X₃₃₈ = isogonal conjugate of X₂₃₃₅₇

• X₃₃₈ = isotomic conjugate of X₂₄₉

• X₃₃₈ = anticomplement of X₃₄₉₉₀

• X₃₃₈ = X₂₆₄-Ceva conjugate of X₅₂₃

• X₃₃₈ = cevapoint of X₁₁₅ and X₁₂₅

• X₃₃₈ = X₁₂₅-cross conjugate of X₃₃₉

• X₃₃₈ = pole wrt polar circle of trilinear polar of X₂₅₀ (line X₁₁₀X₁₁₂)

• X₃₃₈ = polar conjugate of X₂₅₀

• X₃₃₈ = X₆-isoconjugate of X₁₁₀₁