X₂₄₈

X₄-LINE CONJUGATE OF X₁₃₂

X₂₄₈ = crossdifference of every pair of points on line X₁₁₄X₁₃₂

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

X₂₄₈ (X₄-LINE CONJUGATE OF X₁₃₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 32}, {39, 54}

• Related Centers: X₄ (ORTHOCENTER), X₁₃₂ (∩X₄X₃₂), X₃₂ (3rd POWER POINT), X₃₉ (BROCARD MIDPOINT), X₅₄ (KOSNITA POINT)

Trilinears: \(\sin 2A \sec(A + \omega ) : \sin 2B \sec(B + \omega ) : \sin 2C \sec(C + \omega )\)

Barycentrics: \(\sin A \sin 2A \sec(A + \omega ) : \sin B \sin 2B \sec(B + \omega ) : \sin C \sin 2C \sec(C + \omega )\)

Search Value (6, 9, 13): \(1.299410512757\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines11 lines

{4, 32}, {6, 157}, {39, 54}, {50, 67}, {65, 172}, {66, 571}, {69, 287}, {72, 293}, {74, 187}, {290, 385}, {682, 695}

▸ Functional Relations12 relations

• X₂₄₈ = isogonal conjugate of X₂₉₇

• X₂₄₈ = crosspoint of X₉₈ and X₂₈₇

• X₂₄₈ = crosssum of X₂₃₂ and X₅₁₁

• X₂₄₈ = crossdifference of every pair of points on line X₁₁₄X₁₃₂

• X₂₄₈ = X₄-line conjugate of X₁₃₂

• X₂₄₈ = trilinear pole of line X₁₈₄X₆₄₇

• X₂₄₈ = crossdifference of every pair of points on line X₁₁₄X₁₃₂

• X₂₄₈ = X₂-Ceva conjugate of X₃₉₀₈₅

• X₂₄₈ = X₉₂-isoconjugate of X₅₁₁

• X₂₄₈ = perspector of conic {A, B, C,X₆₈₅,X₂₀₆₅,X₂₇₁₅,X₁₅₄₀₇,X₁₇₉₃₂}}

• X₂₄₈ = barycentric product X₃*X₉₈

• X₂₄₈ = barycentric product of circumcircle intercepts of line X₃X₅₂₅