X₂₂₅

X₄-CEVA CONJUGATE OF X₆₅

X₂₂₅ = X₄-Ceva conjugate of X₆₅

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

X₂₂₅ (X₄-CEVA CONJUGATE OF X₆₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 4}, {12, 37}

• Related Centers: X₄ (ORTHOCENTER), X₆₅ (ORTHOCENTER OF THE INTOUCH TRIANGLE), X₁ (INCENTER), X₁₂ ({X), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID)

Trilinears: \((\sec A)(\cos B + \cos C) : (\sec B)(\cos C + \cos A) : (\sec C)(\cos A + \cos B)\)

Barycentrics: \((\tan A)(\cos B + \cos C) : (\tan B)(\cos C + \cos A) : (\tan C)(\cos A + \cos B)\)

Search Value (6, 9, 13): \(-0.413795752358\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines15 lines

{1, 4}, {3, 1074}, {7, 969}, {10, 201}, {12, 37}, {19, 208}, {28, 108}, {46, 254}, {65, 407}, {75, 264}, {91, 847}, {158, 1093}, {377, 1038}, {412, 775}, {653, 897}

▸ Functional Relations10 relations

• X₂₂₅ = isogonal conjugate of X₂₈₃

• X₂₂₅ = isotomic conjugate of X₃₃₂

• X₂₂₅ = anticomplement of X₃₄₈₅₁

• X₂₂₅ = X₄-Ceva conjugate of X₆₅

• X₂₂₅ = X₄₀₇-cross conjugate of X₄

• X₂₂₅ = crosspoint of X_i and X_j for these (i,j): (4, 158), (273, 278)

• X₂₂₅ = crosssum of X_i and X_j for these (i,j): (3, 255), (212, 219)

• X₂₂₅ = X_i-beth conjugate of X_j for these (i,j): (4, 225), (10, 227), (108, 1042), (318, 10)

• X₂₂₅ = pole wrt polar circle of trilinear polar of X₃₃₃ (line X₅₂₂X₆₆₃)

• X₂₂₅ = polar conjugate of X₃₃₃