X₁₉₆₃

CROSSSUM OF PU(32)

X₁₉₆₃ = X₁₉₂₉-Ceva conjugate of X₁₉₃₁

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

X₁₉₆₃ (CROSSSUM OF PU(32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {37, 757}

• Related Centers: X₁₉₂₉ (ISOGONAL CONJUGATE OF X₁₇₅₇), X₁₉₃₁ (CROSSDIFFERENCE OF PU(32)), X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₇₅₇ (ISOGONAL CONJUGATE OF X₇₅₆)

Trilinears: \(1/[(a + b)(a + c)] + 1/(b + c)^{2} : :\)

Search Value (6, 9, 13): \(1.511775865541\)

▸ Incident Central Lines5 lines

{1, 1326}, {2, 6}, {37, 757}, {662, 1100}, {894, 1509}

▸ Functional Relations3 relations

• X₁₉₆₃ = X₁₉₂₉-Ceva conjugate of X₁₉₃₁

• X₁₉₆₃ = crosspoint of PU(31)

• X₁₉₆₃ = intersection of tangents at PU(31) to conic {{A, B, C,PU(31)}}