X₂₃₃

X₂-CEVA CONJUGATE OF X₁₄₀

X₂₃₃ = perspector of circumconic centered at X₁₄₀

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

X₂₃₃ (X₂-CEVA CONJUGATE OF X₁₄₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {6, 17}, {5, 53}

• Related Centers: X₂ (CENTROID), X₁₄₀ (MIDPOINT OF X₃ AND X₅), X₆ (SYMMEDIAN POINT), X₁₇ (1st NAPOLEON POINT), X₅ (NINE-POINT CENTER), X₅₃ (SYMMEDIAN POINT OF ORTHIC TRIANGLE)

Trilinears: \([b \cos(C - A) + c \cos(B - A)]\cos(B - C) : :\)

Barycentrics: \((a^{2} (b^{2} + c^{2}) - (b^{2} - c^{2})^{2}) (2 a^{4} - 3 a^{2} (b^{2} + c^{2}) + (b^{2} - c^{2})^{2}) : :\)

Search Value (6, 9, 13): \(48.812271241930\)

▸ Alternate Coordinates1 form

• Trilinears: \(b \sec(A - B) + c \sec(A - C) : :\)

X₂₃₃ lies on hyperbola {X₂,X₆,X₂₁₆,X₂₃₃,X₁₂₄₉,X₁₅₆₀,X₃₁₆₂}}. This hyperbola is a circumconic of the medial triangle, and the locus of perspectors of circumconics centered at a point on the Euler line. It is tangent to Euler line at X₂. (Randy Hutson, March 21, 2019)

▸ Incident Central Lines5 lines

{2, 95}, {5, 53}, {6, 17}, {115, 128}, {122, 138}

▸ Functional Relations11 relations

• X₂₃₃ = isogonal conjugate of X₂₈₈

• X₂₃₃ = isotomic conjugate of X₃₁₆₁₇

• X₂₃₃ = perspector of circumconic centered at X₁₄₀

• X₂₃₃ = complement of X₉₅

• X₂₃₃ = X₂-Ceva conjugate of X₁₄₀

• X₂₃₃ = crosspoint of X₂ and X₅

• X₂₃₃ = crosspoint of X₃₆₃₀₀ and X₃₆₃₀₁

• X₂₃₃ = crosssum of X₆ and X₅₄

• X₂₃₃ = crossdifference of every pair of points on line X₁₁₅₇X₁₅₁₀

• X₂₃₃ = polar conjugate of the isogonal conjugate of X₃₂₀₇₈

• X₂₃₃ = center of circumconic that is locus of trilinear poles of lines passing through X₁₄₀