X₁₄₁₅

X₁₀₁-BETH CONJUGATE OF X₁₀₁

X₁₄₁₅ = crosssum of X₅₂₁ and X₆₅₀

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

X₁₄₁₅ (X₁₀₁-BETH CONJUGATE OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {32, 56}, {101, 109}

• Related Centers: X₁₀₁ (Ψ(INCENTER, SYMMEDIAN POINT)), X₃₂ (3rd POWER POINT), X₅₆ (EXSIMILICENTER), X₁₀₉ (Ψ(INCENTER, CIRCUMCENTER))

Trilinears: \(a^{2}/(\cos B - \cos C) : :\)

Search Value (6, 9, 13): \(0.074130685757\)

▸ Alternate Coordinates1 form

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

▸ Incident Central Lines17 lines

{6, 909}, {32, 56}, {41, 609}, {57, 609}, {65, 172}, {101, 109}, {108, 112}, {198, 478}, {213, 1399}, {571, 608}, {604, 1417}, {651, 662}, {910, 1455}, {919, 934}, {923, 1402}, {1055, 1457}, {1333, 1400}

▸ Functional Relations17 relations

• X₁₄₁₅ = X_i-Ceva conjugate of X_j for these (i,j): (59, 1397), (109, 692), (1262, 56)

• X₁₄₁₅ = X_i-cross conjugate of X_j for these (i,j): (649, 1333), (667, 56), (1397, 59)

• X₁₄₁₅ = cevapoint of X_i and X_j for these (i,j): (32, 667), (649, 1400)

• X₁₄₁₅ = crosspoint of X_i and X_j for these (i,j): (108, 651), (109, 1461), (112, 163)

• X₁₄₁₅ = crosssum of X₅₂₁ and X₆₅₀

• X₁₄₁₅ = crossdifference of every pair of points on line X₁₁X₁₂₃

• X₁₄₁₅ = barycentric product of X₁₃₈₁ and X₁₃₈₂

• X₁₄₁₅ = isogonal conjugate of X₄₃₉₁

• X₁₄₁₅ = trilinear pole of line X₃₁X₁₈₄

• X₁₄₁₅ = X₉₂-isoconjugate of X₅₂₁

• X₁₄₁₅ = barycentric product of PU(102)

• X₁₄₁₅ = polar conjugate of isotomic conjugate of X₃₆₀₅₉

• X₁₄₁₅ = perspector of unary cofactor triangles of outer and inner Garcia triangles

• X₁₄₁₅ = barycentric product X₁*X₁₀₉

• X₁₄₁₅ = barycentric product X₃*X₁₀₈

• X₁₄₁₅ = trilinear product X₆*X₁₀₉

• X₁₄₁₅ = trilinear product of circumcircle intercepts of line X₆X₄₁ (or of circle {{X₁,X₁₅,X₁₆}} (V(X₁))