X₃₁₂₀

DANNEELS PERSPECTOR FOR X₁₀

X₃₁₂₀ = reflection of X₉₀₂ in X₃₀₁₁

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

X₃₁₂₀ (DANNEELS PERSPECTOR FOR X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {902, 3011}

• Related Centers: X₉₀₂ (CROSSPOINT OF X₆ AND X₁₀₆), X₃₀₁₁ ((NAGEL LINE)∩(ORTHIC AXIS))

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(b + c)(b - c)^{2}\)

Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

Search Value (6, 9, 13): \(1.958119495676\)

▸ Incident Central Lines26 lines

{1, 149}, {2, 846}, {7, 2648}, {11, 244}, {27, 2206}, {31, 1836}, {38, 2886}, {42, 226}, {58, 79}, {109, 2006}, {115, 125}, {225, 1042}, {321, 2887}, {334, 1978}, {442, 2292}, {516, 902}, {614, 990}, {726, 3006}, {851, 1284}, {899, 908}, {946, 1201}, {986, 2476}, {1109, 2632}, {1365, 2611}, {1834, 2650}, {2170, 2969}

▸ Functional Relations14 relations

• X₃₁₂₀ = reflection of X₉₀₂ in X₃₀₁₁

• X₃₁₂₀ = X_i-Ceva conjugate of X_j for these (i,j): (10, 523), (27, 649), (79, 513), (86, 514), (226, 661), (313, 1577), (1086, 3125)

• X₃₁₂₀ = cevapoint of X₁₁₅ and X₂₆₄₃

• X₃₁₂₀ = X₂₆₄₃-cross conjugate of X₃₁₂₅

• X₃₁₂₀ = crosspoint of X_i and X_j for these (i,j): (10, 523), (65, 513), (86, 514), (313, 1577), (321, 693), (1086, 1111)

• X₃₁₂₀ = crosssum of X_i and X_j for these (i,j): (21, 100), (42, 101), (58, 110), (163, 2206), (692, 1333), (1110, 1252)

• X₃₁₂₀ = crossdifference of every pair of points on the line X₁₀₁X₁₁₀

• X₃₁₂₀ = isogonal conjugate of X₄₅₇₀

• X₃₁₂₀ = isotomic conjugate of X₄₆₀₀

• X₃₁₂₀ = intersection of tangents to Steiner inellipse at X₁₁₅ and X₁₀₈₆

• X₃₁₂₀ = crosspoint wrt medial triangle of X₁₁₅ and X₁₀₈₆

• X₃₁₂₀ = complement of X₄₄₂₇

• X₃₁₂₀ = X₁₀-isoconjugate of X₁₁₀₁

• X₃₁₂₀ = barycentric product X_i*X_j for these {i,j}: {10, 1086}, {514, 423}