X₂₁₇₅

X₂-ISOCONJUGATE OF X₈₅

X₂₁₇₅ = X₇-isoconjugate of X₇₅

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

X₂₁₇₅ (X₂-ISOCONJUGATE OF X₈₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {25, 181}, {31, 184}

• Related Centers: X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₁₈₁ (APOLLONIUS POINT), X₃₁ (2nd POWER POINT), X₁₈₄ (INVERSE OF X)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₈₅

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

Search Value (6, 9, 13): \(1.140099352073\)

▸ Alternate Coordinates2 forms

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \cot(A/2) \sin^{3} A\)

• Trilinears: \(a^{3}(a - s) : b^{3}(b - s) : c^{3}(c - s)\)

▸ Incident Central Lines22 lines

{6, 692}, {9, 2330}, {25, 181}, {31, 184}, {32, 560}, {41, 1253}, {42, 2273}, {48, 2223}, {55, 219}, {154, 1460}, {182, 238}, {213, 1973}, {344, 1083}, {601, 1092}, {760, 1760}, {1036, 1682}, {1037, 1362}, {1401, 1473}, {1631, 2245}, {1691, 2176}, {2056, 2162}, {2209, 2210}

▸ Functional Relations13 relations

• X₂₁₇₅ = isogonal conjugate of X₆₀₆₃

• X₂₁₇₅ = complement of X₂₁₂₈₀

• X₂₁₇₅ = anticomplement of X₁₇₀₄₇

• X₂₁₇₅ = X_i-Ceva conjugate of X_j for these (i,j): (31, 6), (31, 32), (2194, 41)

• X₂₁₇₅ = X₁₉₁₈-cross conjugate of X₂₂₁₂

• X₂₁₇₅ = crosspoint of X_i and X_j for these (i,j): (31, 41), (55, 607)

• X₂₁₇₅ = crosssum of X_i and X_j for these (i,j): (7, 348), (8, 344), (74, 85), (349, 1441)

• X₂₁₇₅ = crossdifference of every pair of points on line X₉₁₈X₃₂₆₁

• X₂₁₇₅ = X₇-isoconjugate of X₇₅

• X₂₁₇₅ = barycentric product of PU(93)

• X₂₁₇₅ = Lozada perspector of X₆

• X₂₁₇₅ = perspector of tangential triangle and cross-triangle of intouch and tangential triangles

• X₂₁₇₅ = trilinear product of vertices of Apus triangle (the extraversions of X₅₆)