X₃₇₈₇

X₁₁₉₆com[INVERSE(nT(a², a² - c²))]

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

X₃₇₈₇ (X₁₁₉₆com[INVERSE(nT(a², a² - c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {184, 187}, {32, 394}

• Related Centers: X₁₈₄ (INVERSE OF X), X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₃₂ (3rd POWER POINT), X₃₉₄ (-CEVA CONJUGATE OF X₃)

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{2} + c^{2})(b^{2} + c^{2} - 3a^{2})\)

Search Value (6, 9, 13): \(-1.427002198385\)

▸ Incident Central Lines14 lines

{32, 394}, {39, 3051}, {51, 3231}, {184, 187}, {323, 1627}, {511, 1196}, {800, 3289}, {1194, 2979}, {1351, 1611}, {1501, 3292}, {1692, 1993}, {2056, 2076}, {3053, 3167}, {3060, 3291}