X₃₉₃₃

X₃₂com[INVERSE(n(TANGENTIAL TRIANGLE))]

X₃₉₃₃ = crossdifference of every pair of points on line X₂₄₈₉X₃₈₀₄

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

X₃₉₃₃ (X₃₂com[INVERSE(n(TANGENTIAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Circle: Circumcircle (circumcircle) — Passes through vertices A, B, C; centered at X₃ CIRCUMCENTER

• Central Lines: {3, 69}, {5, 76}

• Related Centers: X₃ (CIRCUMCENTER), X₆₉ (SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE), X₅ (NINE-POINT CENTER), X₇₆ (3rd BROCARD POINT)

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

Search Value (6, 9, 13): \(5.794026184777\)

▸ Alternate Coordinates1 form

• Barycentrics: \(\csc A \cot A \sin(A + \omega ) : :\)

▸ Incident Central Lines27 lines

{3, 69}, {5, 76}, {11, 3760}, {12, 3761}, {30, 315}, {32, 524}, {39, 141}, {99, 550}, {140, 183}, {187, 3630}, {194, 3314}, {264, 1595}, {304, 337}, {305, 1368}, {316, 3627}, {350, 496}, {394, 441}, {427, 1235}, {495, 1909}, {538, 626}, {549, 1078}, {574, 3631}, {980, 1211}, {1007, 1656}, {1353, 3398}, {1930, 3665}, {3673, 3705}

▸ Functional Relations4 relations

• X₃₉₃₃ = isotomic conjugate of X₃₂₀₈₅

• X₃₉₃₃ = complement of X₇₇₅₄

• X₃₉₃₃ = anticomplement of X₅₃₀₅

• X₃₉₃₃ = crossdifference of every pair of points on line X₂₄₈₉X₃₈₀₄