X₃₉₇₈

X₆₉₄com[INVERSE(n(1st BROCARD TRIANGLE))]

X₃₉₇₈ = complement of Steiner-circumellipse-inverse of X₃₉

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

X₃₉₇₈ (X₆₉₄com[INVERSE(n(1st BROCARD TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 39}, {75, 256}

• Related Centers: X₂ (CENTROID), X₃₉ (BROCARD MIDPOINT), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₂₅₆ (1st SHARYGIN POINT)

Barycentrics: \(b^{2}c^{2}(a^{2} - bc)(a^{2} + bc) : :\)

Search Value (6, 9, 13): \(14.551202379820\)

▸ Alternate Coordinates1 form

• Barycentrics: directed distance of A to line PU(1) : :

▸ Incident Central Lines15 lines

{2, 39}, {6, 706}, {75, 256}, {83, 1207}, {99, 237}, {290, 325}, {308, 3589}, {315, 1899}, {316, 512}, {524, 670}, {561, 3765}, {671, 886}, {694, 698}, {702, 1084}, {1215, 1237}

▸ Functional Relations9 relations

• X₃₉₇₈ = isogonal conjugate of X₉₄₆₈

• X₃₉₇₈ = isotomic conjugate of X₆₉₄

• X₃₉₇₈ = complement of polar conjugate of isogonal conjugate of X₂₃₁₇₄

• X₃₉₇₈ = complement of Steiner-circumellipse-inverse of X₃₉

• X₃₉₇₈ = anticomplement of X₃₂₂₉

• X₃₉₇₈ = perspector of conic {{A, B, C,PU(11)}}

• X₃₉₇₈ = trilinear pole of line PU(1) of 1st anti-Brocard triangle

• X₃₉₇₈ = trilinear pole of PU(133) (line X₈₀₄X₅₉₇₆)

• X₃₉₇₈ = X₆₉₄-of-1st-anti-Brocard-triangle